IF the float is used to control the salt dose, then the control valve has a problem in not delivering the water to the brine tank. It could be a bad brine valve but more likely is a major valve problem.
IF the float is part of a safety brine system, meant to prevent tank overflow, then the float has nothing to do with the cause of the problem unless stuck in the up position.
IF the control valve has Pre fill as opposed to Post refill (most older controls), then the water in the tank between regenerations will only be a few inches deep most of the time except for two hours while the water dissolves salt before the beginning of the brining cycle starts on the night a regeneration happens.
So the question is... should there be more water in your brine tank than there is? Or... what is/isn't the softener doing wrong?