My daughter has been caring 24/7 in her home for our elder friend for 3 years. Does he have to pay when he is gone to rehab for 1 to 2 months?

It depends on the contract? arrangement? they made. For example, centre-based child care often has to be paid even if it isn’t needed for days or a couple of weeks, because the place can’t be back-filled and all the costs continue. For a longer break, most times a child care booking would be cancelled. For this question to come up, my guess would be that the income is important financially for your daughter. Any bill certainly shouldn’t cover food and other consumables that aren’t being used, but they might agree a ‘holding charge’ to keep the ‘place’ open’.