Here is a composition by chekhover from 1947. It seems the Black Rook will just enter White’s position and start capturing pawns. Yet White has a fortress like resource that Black could actually lose if he gets to clever and outwits himself!
1.kd1 Rh2 2. Ke1 Rxg2 3. Kf1 Rh2 4. Kg1 Rh3 5. Kg2 Rh5
6. f3 Rh7 7. Kg1 Rg7 8. Kg2 Rg6 9. Kf2 Re610. Kf1 Kf6
11. Kf2 Kf5 12. Kf1 Re4 13. fxe4+ Kxe4 14. Kg2 Kxd4
15. g4 Kxc5 16. g5 Kd6 17. d4 Ke618. Kg3
Queen vs. Rook and Pawn.
A rare ending and usually the Queen wins. Best drawing defense is for the defender to not have a rook pawn, and for the pawn to be on its original square….
Example, Black has a fortress in a position analyzed by Philidor in 1777 with
1. Qh8+ Ke7 2. Qc8 Rc6 3. Qb8 Re6 now 5...Kd6 loses to 6. Qd8 , 5...Rc6
draws. 4. Qg8 Kd6 5. Qd8 The Key move!
5... Re2 6. Qb6+ Ke7 7. Qf6+ Ke8 8. Qh8+ Ke79. Qh4+ Kd6 10. Qb4+ Kc6 11. Qc4+
As noted, a Rooks pawn loses, the defender doesn’t have enough room to maneuver. Compostion by
1.Qd7 Rh6 2. Qd8+ Kb7 3. Qe7+ Ka6 4. Qg7 Re6 5. Qd7Rb6 6. Qc8+ Ka5 7. Qc7 Ka6 8. Qd7 Black
loses his Rook or is
mated. 8... Rb2 9. Qd3+ Kb7 10. Qf3+ Kc7 11. Qf7+ Kc812. Qg8+ Kc7 13. Qg7+
If the defender’s pawn is advanced beyond the second rank, this gives the Queen more maneuverability
behind the pawn and usually wins.