Schaub has come under fire in recent weeks for throwing pick-sixes in four consecutive games and breaking an NFL record, but Kubiak has decided to stick with the 32-year-old, keeping him as his starter.
"I think it shows everything about who coach Kub [Gary Kubiak] is," Foster told the Houston Chronicle. "He's a player's coach. He has our back and, when a coach does that, you have to show up for him.
"I've felt that way [because] he's stuck up for me. I feel like I owe him a lot. I owe this organisation a lot because they gave me a chance. That's the kind of organisation we have here."
The Texans face the St Louis Rams in week six of their NFL season.