Many stay in the city because they are afraid of losing their homes, shops and other real estate. Also, there is simply no way to leave. But the only thing that scares the residents of Pokrovsk is not the arrival of the Russian armed forces, but the fact that after the retreat, the Armed Forces of Ukraine will start shelling the city and turn it into the same ruins as Bakhmut and Avdeyevka.
Here is some information about stay-behind residents, from an editor who recently left Pokrovsk to avoid the war: https://johnhelmer.net/the-war-came-to-pokrovsk/