Do people with PESEL UKR status have to register in Poland? And what if they fail to check in if there is an obligation to do so?

The applicable regulations provide for the possibility of imposing a fine for failure to register on a foreigner who does not have EU citizenship. In practice, however, such fines are not imposed, and due to the exceptional situation related to the admission of refugees from Ukraine to Poland, you should not be afraid of a fine if you do not register.