Praise be to Allah.
There is nothing wrong with a wife letting her husband off paying the Mahr, because Allaah says (interpretation of the meaning):
“but if they, of their own good pleasure, remit any part of it to you, take it, and enjoy it without fear of any harm (as Allâh has made it lawful)” [al-Nisaa’ 4:4]
This deferred payment becomes due in the case of divorce after the consummation of the marriage, even if the time-period involved is short – unless the woman demands khul’ [a kind of divorce instigated by the wife] and gives up her right to the money, as a compensation to the husband for leaving him. This is OK is the khul’ is done for a legitimate reason and not just for the sake of getting the money. Allaah says (interpretation of the meaning):
“… and you should not treat them with harshness, that you may take away part of the Mahr you have given them, unless they commit open illegal sexual intercourse…” [al-Nisaa’ 4:19]
It is permissible for the husband to say “I will give you such and such as a Mahr”, even if he does not own it; he should explain to them that this is to be paid later rather than sooner, and it will be a debt that he owes. And Allaah knows best.