Here is a real example. My niece wound up with 3 kids, divorced, with inconsistent child support payments. So she went on food stamps. She was looking for a better job. She found one, interviewed, and they wanted to hire her. But the salary that they offered was $0.50/hour too much for her to stay on food stamps, and was less than her current job. Thanks to union regulations, the person who wanted to hire her couldn't pay her less than the standard salary. The result is that she did not take the job.
A common result when Congress takes note of perverse incentives like this is that they introduce a more complex program with specific terms that address specific problems that emerged. The problem is that by creating more brackets and more complex rules you usually create MORE cliffs with perverse incentives (though the perverse incentive at each cliff tends to be less).
Another solution is to introduce rules that attempt to identify people who are "abusing the system" and punish them. So, for example, you can only be on welfare for a limited time because people got outraged that single mothers wound up on welfare for a long time. However those single mothers were acting that was in part because they were better off on welfare looking after their own kids than they were in a low end job and paying for daycare.
Stereotypically the first type of solution is characteristic of Democrats and the second of Republicans. But the truth is that both parties do a lot of both solutions.