If the person who moved out of the home is still contributing to the payment of the house, will that be considered as equity towards ed at the time of the ed settlement or divorce?
For the purposes of evaluating division of property there are two factors at play:
1. The matrimonial period is deemed over as of the date of the first filing in the divorce case.
2. Any division is done on an "equitable" basis, that means, the court tries to do what's fair. So if you're still making contributions such as mortgage payments after leaving the house, you have a chance at recouping some of that money in the form of an increased equitable distribution.
However, there are much better ways to handle things - something you should discuss in a consultation with a matrimonial attorney. The cost of the consultation is almost invariably far less than the cost of a mistake.