To encourage or aid someone in something considered unworthy is to...

The term that describes the act of encouraging or aiding someone in an endeavor that is considered unworthy is "abet." This verb is often associated with crime or wrongdoing, implying that the person providing support is facilitating undesirable actions. For example, if someone helps another person commit a robbery, the helper is said to abet the crime.

The other terms do not carry the same connotation or meaning. "Abstain" refers to the act of deliberately choosing not to engage in an activity, while "abrogate" means to repeal or do away with a law, right, or formal agreement. "Abate," on the other hand, means to become less intense or widespread, often used in the context of reducing something undesirable, like noise or pain. Therefore, "abet" is the only choice that accurately captures the idea of providing assistance in a negative context.