If someone comes to the US on a tourist visa for 6 months, but then sends documentation to extend their stay based on another status, can they stay while it's b

If someone comes to the US on a tourist visa for 6 months, but then sends documentation to extend their stay based on another status, can they stay while it's being evaluated, even if it takes more than 6 months? If it is rejected, how soon afterwards would they have to leave, and will their stay be held against them?