Not a lawyer.
Typically, your employer must pay you your week's pay for any week in which you perform work. An exception to this requirement may be that they can withhold pay for any day in which you perform no work. Also, the employer can make you use vacation or other paid time off for hours not worked on any given day, without crediting them back if you make up the time later.
If your 20 hours were:
2 days of 10 hours each, your employer must pay you for two days;
2 normal days and a half day, your employer must pay you for three days, possibly charging you 4 hours of vacation/paid time off if you have any available
5 half days, your employer must pay you for five days, possibly charging you 20 hours of vacation/paid time of if you have any available
The correct solution to people working part days without sufficient accrued PTO is disciplinary action up to and including termination, but you cannot simply dock pay (except for full days missed within a week).
Note also that in the same way your employer can "demand" you work 80 hours per week, you can "demand" that you only work 20 hours per week for the same pay and benefits. You are both (typically) free to negotiate and walk away at any time.