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Now that you have already lost the will contest, the number of options have now reduced for your parents. Unless your parents discover some evidence of ownership that could be used to appeal the previous court decision and get the judgment and thus the sale vacated, your parents' only shot is to object to the eviction suit. In objecting to the eviction they could get 1 or 2 continuances as the NYC housing court is busy, but quite honestly, the most they can buy themselves on an eviction is maybe 2 months, 3 months maximum
An eviction suit, once ownership is decided, moves quickly even with continuances.
Your parents could hire an attorney to challenge the sale as invalid and take the new owners to court and argue their purchase was not a valid or legal purchase. The problem with this tactic is that while it would buy them maybe a year or more, when they lose the case, they will be looking at paying their own attorney's fees of likely about $10,000 PLUS the other party's attorney's fees. So it may not be a cost effective means of keeping them in the property.