Is it permissible for me to sell my residency in Europe to someone who is likely to use it for illicit purposes, such as obtaining an interest-based loan or evading taxes, in exchange for money?

Selling residency permits and visas outside legal frameworks is impermissible. However, if the sale of a residency permit is customary and does not violate the law, then any illicit gains the buyer might make do not harm the seller, as long as the seller does not know with certainty what the buyer intends to do.