In general, stray cats need to eat when following people. Following people may provide food, or it may be due to their curiosity, which is well-known among cats. Companionship may be that cats need more companionship, or they may feel lonely and want you to play with them. If its hungry, it may get something to eat by following people. You can feed it some food.
If the cat is injured, it may feel uncomfortable. It may be injured somewhere and needs your help and care. Curiosity cats are also famous for their curiosity. As the saying goes, curiosity kills cats. Cats are a species with extremely strong curiosity, and they may follow you purely to satisfy their own curiosity. Silently observing you, pondering what I dont know inside! Patrol cats may be patrolling their territory to see if they have been invaded by outsiders and if there are any suspicious species around them. Cats need to patrol their territory several times a day to leave their scent. If you see them following you, occasionally pressing their face against you or furniture, then they are patrolling. Everything here belongs to it, including you!