Fat cells can move and help in repair of a wound, seen in fruit flies:

https://cosmosmagazine.com/biology/fat-cells-swim-and-block-wounds

"At least in fruit flies, fat cells have been found to exhibit several previously unknown and surprising behaviours geared to healing wounds and fending off infection.

"The behaviours are surprising because they involve properties that fat cells – considered to be one of the most uncontroversial, best examined and, frankly, unexciting cell types around – had not been remotely suspected of possessing.

"The cells, it turns out, can swim – really swim, moving along by flexing and contracting. What’s more, they do so in response to some form of unknown signal – something that has so far eluded the scientists searching for it.

***

"The fat cells can be seen propelling themselves forward, using wave-like contortions, towards the site of the injury. This is doubly interesting. Until now, fat cells were not thought to be capable of moving under their own power, nor were they thought to play any role at all in wound repair.

***

"Martin and his colleagues filmed the fat cells moving directly to the wound site and bunching up within it, sealing it off from the outside. At the same time, they cause debris from the opening to be wafted away from the critical zone, into the waiting maws of immune system cells.

"The fat cells then remained at the wound until healing was complete, at which point they detached and swam away.

***

“We had to be sure that they weren’t just drifting and then sort of sticking at the wound site,” says Martin. “And we had to rule out that they weren’t just being sort of sucked to the wound by fluid coming out of the hole, much like if you tossed a flannel in a bath and then took the plug out.”

"To do so, they genetically engineered fruit fly fat cells that lacked the actin and myosin fibres, and then repeated the experiment. The modified cells didn’t move at all, indicating that the “natural” versions were indeed actively migrating.

"How the cells “know” to move to a wound is unknown, but Martin and his colleagues have ruled out the possibility that they are responding to signals sent by the immune system. The fat cells, they established, still move towards wounds even if immune cells aren’t present.

"Once at the site, however, in normal fruit flies, the two cell types clearly collaborate.
“So fat cells and immune cells probably are important as a team, both in a healthy situation, like healing a wound, and in a pathology situation, like cancer,” he says.

Comment: My interpretation is that these fat cells are programmed to act in this purposeful manner and how they 'know' where to go is from a still to be discovered molecular signal which hey the swim and follow. I can predict dhw's answer to this.