It happens. The AI rarely, if ever, rotates their squad so you can use it to your advantage although I am not certain of how much of an advantage it would be on an individual player.
In terms of individual player performance I am not sure how it affects the attributes, although I would guess that their pace/acceleration, jumping reach and physicals are somewhat affected as are decisions. So all I can offer is what I am wary of in my own players.
They will be more susceptible to injuries, their decisions won;t be as good as when fully fit, there ability to chase, tackle and get in the right position will be hampered as will shooting and passing accuracy over distances.
So, if facing a fatigued team and if your squad is familiar/ able with the tactic I would slow the tempo and retain possession for maybe the first hour - make them chase the ball. Play wider. Maybe play a bit deeper and wider- basically stretch the area of the pitch you use.
Then, up the tempo, close down, tackle harder should turn the screw for the last half hour.
Make them burn off what little energy they started with and then steam-roller them into submission.