They generally don't. The person who nominates the celebrity (who can be literally anyone, but is often the celebrity themselves) pays $40,000 up front for installation and maintenance. In theory taxes would pay for maintenance on older stars, with the idea that the tourists they bring to the area pump more money into the economy than it costs to pay for the stars' upkeep (and many of the celebs with stars sign deals that allow local businesses to sell merch with their likeness on it as well), but around 20% of the stars are cracked, broken, stained, and otherwise in disrepair because Hollywood doesn't actually spend any money to fix them. To get a damaged star fixed on the Walk of Fame a private party generally has to pay the installation cost again, especially if it's an older deceased celeb. It's possible the city maintains Trump's in situations like this because it is a tourist draw in and of itself (no such thing as bad publicity), but I don't know for sure.
