This is a pun on 'recovered' which means to return to a normal state of health, mind, or strength,  like you'd want to recover after falling into a machine. But it's also being used because upholstry is the work of providing furniture, especially seats, with padding, springs, webbing, and fabric or leather covers. So in this case the speaker was covered in fabric
The man who fell into an upholstery machine is fully recovered .