After completing the quest, being back to Finch Farm with Jake Finch, and the last one having thank you, you could have Jake Finch stuck in that position, in that speach, and even if you assign bed or work to him, he will be stuck there.

The problem is Preston Garvey.

It can happen if you havent joined the Minutemen. Preston Garvey will be stuck in his request to join them, no other option available for him, you cant assign him to a bed for example. And he will no thank you to having free Jake. So, you are unable to end the Mission and Jake will be stuck too in his thanks to you.

Solution: Joining the Minutemen will solve both problems, preston Garvey will be available for assignements again, and if you come back to Finch Farm you will find Jake, and old Aberbathy too, unstuck finally.

Yup. I ran in to that. Once I did the initial Castle quests and Preston went back to Sanctuary, problem solved.