Is it permissible to purchase inoperable government bakery equipment slated for disposal, with the intention of repairing and operating it in a bakery to serve the people, and what is the legitimate Shar'i method for purchasing it?

If the equipment is abandoned and the institution does not want it, then it is permissible to take it and benefit from it, as long as its use does not cause harm. However, if the institution is benefiting from it and has not given permission for it to be taken, then the gatekeeper is not allowed to take it, nor is it permissible to purchase it from him; because it was not acquired through a legitimate means, and whoever buys something that has been usurped or stolen is like the usurper.