They won't 'get stuck' in your washing machine.
I have 4 tanks and run 5 or 6 filter socks all the time. I save dirty socks until I have a full load for the washer (about 25 to 30). I do a wash with an OxyClean type cleaner, then a 2nd wash with bleach, then a 3rd wash with just water. I pull the socks after the spin cycle and then run some bleach in the rinse cycle just to get the washing machine cleaned out for clothes.