Abraham Lincoln and William Berry entered into a partnership as owners of a general store in August 1832, buying a larger building in January 1833 and obtaining a liquor license in March 1833.  But they were poor businessmen, and many sources report that Lincoln was more interested in reading and talking, while Berry was more interested in helping himself to the liquor inventory. They started the business using promissory notes because they didn't have cash, and the debts kept piling up. The business was clearly failing, and Lincoln sold his interest to Berry in April 1833.

Berry subsequently sold out to the Trents in return for promissory notes. No one seems to know the date or the sales price, or even which Trents bought the business. Two additional Trents, Henry and William/Williamson, had arrived in the New Salem area by February 1833 (the Collected Works of Abraham Lincoln pg 17-18 shows their names on a petition at that time), and they were still there in August 1836. Meanwhile Martin Trent had left New Salem at an unknown date, and died in Iowa before April 1836.  

Tarbell pg 187-188 says the purchase was in early 1834. It's generally agreed that the sale really did take place, and that the Trents didn't succeed at the business.  There's apparently no documentation for when they gave up and what happened next, with some sources saying that they skipped town during the night just before the promissory notes were due, and other sources saying that they sold the business.   

There is reason to be suspicious of the "skipping town" story. The Trents obviously left New Salem at some point, but a general exodus had begun by the time the Trents left in 1836 because it was hard to make a living there, and everybody was gone by 1840. Alexander Trent remained in the general area until his death in 1862, and apparently wasn't hard to find since he was targeted in a debt lawsuit the following year. Abraham Lincoln was the plaintiffs' lawyer in the 1837 case, and had the opportunity to deal with any other legal issues involving the Trents.

Thomas pg 37 says that John McNeil bought the Lincoln-Berry store on an unspecified date after the Trents failed, and moved it to Petersburg in 1837. The Lincoln Digital Library has a biography of Alexander Trent that says nothing about skipping town or the store failure, possibly because there is no documentation for these events. Everything else on the page is well documented.

New Salem Memorial pg 145 says "it is not known when they [the Trents] left New Salem, but Alexander made his home in Petersburg during the 1840s". It also reports that the 20th century excavations for the Trent cabin found all the original stone piers in place, and it was the most complete foundation uncovered.

Burlingame Chapter 3, page 257-263 goes into detail about Lincoln and Berry's mismanagement of the store, and a footnote on page 263 talks about creditor E.C. Blankenship who wrote to Lincoln in 1860 saying "I find due me in judgment a note assigned me by Lincoln & Berry on Trent 15th March 1836 $148.22... nothing could at any time be made out of the Trents Martin died some years before I left Springfield insolvent as his Father told me."  This implies that Martin Trent was one of the store owners. Berry died in 1835, and it's not clear who assigned the note in 1836.  Interestingly, the chapter doesn't mention the Trents' purchase of the Berry-Lincoln store.

The Trents leave New Salem

Alexander Trent was still in New Salem on August 1, 1836. Lincoln was running for reelection to the Illinois House of Representatives as a Whig, and a Lincoln Lore article on that day's election reports that "The Trent brothers' cabin to the south was full of Democrats. Alexander, Henry and William Trent voted for May and, with one exception, for the Democratic candidates for the lower house. Alexander Trent, a veteran of Lincoln's company in the Black Hawk war, split his ticket to vote for his old captain." This article was written in 1981, a century and a half after the election. The Trent males were married with children, so it would have been a very crowded house if they were all living together in the same small cabin.  The election district probably covered more than just the town of New Salem, so some of the family members may have been living nearby but not in the same house.

The Trents were apparently gone by November 1836. Page 3 of the Lincoln Lore article reports that their former home was probably the poll site for the November election, and was currently occupied by Caleb Carman.

After New Salem

This wasn't their last encounter with Abraham Lincoln. JSTOR reports on a case called Ellis et al. v. Trent et al., which began in 1837 (the year after the Trents left New Salem), with Lincoln working for the plaintiffs.  Alexander Trent was obviously one of the defendants, with the "et al" possibly being other family members. It's not clear whether the case was related to the store business or some other debt. The case began over a note for $48.32, with $93 finally being collected sixteen years later. Proof that it was possible for determined people to successfully pursue the Trents for debt.

The article goes on to describe land fraud charges against Alexander Trent that emerged as part of this case in 1847, with Lincoln still working for the plaintiffs. The Lincoln Digital Library also mentions this part of the case. The plaintiffs had just discovered that Alexander Trent fraudulently conveyed land to his son to avoid paying the original judgment. After several years of legal machinations, the court ordered the land to be sold in 1853 to pay the debt.

Other connections

The Trents also have an indirect link to Lincoln through the Cogdal family.  It seems that only Elijah Cogdal has actually been identified as a resident of New Salem. But Elijah's brother Isaac Cogdal lived nearby in Rock Creek, and claimed to have known Lincoln since Lincoln first arrived in New Salem in 1831. Cogdal was admitted to the bar in 1860 (at the age of 48!), saying that Lincoln had encouraged him to study law. It's not clear how often Codgal and Lincoln would have seen each other after Lincoln moved to Springfield, since Codgal didn't leave the area and there would have been at least 20 miles between them. 

Cogdal claimed to have asked Lincoln about alleged sweetheart Ann Rutledge in 1861, and Lincoln declared his undying love for her.  Northern Illinois University seems to have the most complete transcript. Ann died of typhoid in New Salem way back in 1835, and there's little evidence of any relationship between her and Lincoln. It's widely suspected that Cogdal was not telling the truth about Ann Rutledge (Tripp), and there's no word on how reliable the claim is about Cogdal studying law because of Lincoln; but it's generally accepted that Cogdal really did know Lincoln. The Trent connection is that Williamson Trent's daughter Louisa married Isaac's brother John Cogdal. Another daughter, Susanna, married Isaac's brother Joseph, and they named one of their sons Isaac.