Yes, it may bias a jury against someone, but sometimes those details are necessary.

My uncle used to run a furniture store in Dallas. One night a guy broke in there. He cut himself on some glass. He sued my uncle for his injuries. My uncle was not allowed to bring up the fact that the man was commiting a crime when he was injured. The criminal won the suit.
Those details would have let the truth come out. Instead we have a jury that ruled against my uncle without the right information. The accident was entirely preventable. The criminal failed to steal from my uncle through illegal means, so he got it through the courts.

This is definitely urban legend territory. In fact, I just went to Snopes, and she dismisses a variant of that story as bogus.

The commission of a felony is germane in such a case and would never be excluded by the court. Part of any type of "slip & fall" suit is establishing time and place.

Now, that does not mean a criminal cannot sue for injuries sustained while breaking the law, anyone can sue anyone, for any reason. Whether a judge/jury will buy it is a different story.

Another issue would be whether the guy breaking in had actually been tried and convicted of a crime. If he was tried and acquitted, or never charged, then claiming he broke in might not be admissible, and could possibly be actionable in and of itself as defamatory.

Basically it was a Corporate council for Chicago, spent the entire trial violating court orders on motuon in limine, then called my black client lazy, thought his crippling back injury like winning the lottery and called a lawsuit a ghetto lottery ticket. I lost the trial since I drew a bad venire and could only seat 3 black jurors.

Reversed on appeal, and Eddie Burke signed off on a low 7 figure settlement thereafter.

The lawyer was hyperconnected (his brother was a head of a city department.) Got appointed to the bench shortly thereafter, then won an uncontested appellate court election . When he retires in a few years at 55 he will have, by my estimation a 250k pension.

Can you tell I'm still hot?

Even if it is costing us taxpayers $250k/year. That's some kind of sweet retirement package you got for judges in Chicago.