As the others pointed out, "claiming themself" is not an optional thing.  If the daughter was ELIGIBLE to claim the parent as a dependent in 2020, it seems like the parent may have committed tax fraud.  If the daughter wants to claim the parent in 2021, you need to make sure that she actually qualifies to claim the mom.

In answer to your question:

• The law gave direction to the IRS to provide rules to avoid this sort of double-dipping of the $1400.
• As of now, the IRS has NOT provided any rules to avoid double-dipping, and the 1040 Instructions do not mention anything about it.