1. No, small HELOC, under $10,000
Assuming that the subject property is worth MORE THAN $10,000, which seems very likely in New York State, it would then seem that you are absolutely OUT OF YOUR MIND in trying to defend a foreclosure action instead of selling the subject property.
In defending against a foreclosure action rather than FINDING THE CASH AND SETTLING OR selling the subject property, you are going to (a) expose the the estate to legal fees well in excess of $10,000, and (b) cause this property to be sold at a foreclosure sale at a price which will probably be at least 25% below market value and possibly even a far steeper discount.
Maybe you are just planning on bidding at the property at the commissioners sale so that you can steal the equity from the other heirs. The trouble with this strategy is that in failing to sell the property for its actual market value to realize its equity, you are probably breaching your fiduciary duties to the other heirs.
If you think that a likely outcome is ownership of this property, stripped of the HELOC lien, you are simply delusional. If you think that you could succeed in even forestalling the foreclosure long enough to make resisting foreclosure a good strategy, you are simply delusional.
Before, I thought that we ought not help you because you have been rude and less than forthcoming. Now, it seems rather clear that you are simply out of your mind!
Are any of your nieces and nephews sane?