The problem isn't 'when she passes' but NOW.
In most states the house is already in jeopardy. You need to consult with a MA attorney (assuming that is where the house is) to both verify what needs to be done to prevent a tax sale, and also what can be done to replace your aunt as trustee and remove her from the house ASAP. I hope this is not too late, but, for example in Michigan, property with taxes two years in arrears will be sold at tax sale and there is no way to recover the property once that sale is perfected.
I'm surprised that there hasn't been a tax sale already!! This sounds like a clear breach of fiduciary duty.
You should VERY seriously consider covering the tax bill so that you don't lose the property. At the same time, you need to get your aunt removed as trustee ASAP and to get a court order which directs her to reimburse you for the all the money you need to pay to keep the house. If the facts are as you say, there's a good likelihood that the court would order your aunt to pay some or all of the legal bill as well.
Hire a good attorney ASAP.
It may be that your Aunt has arranged for a deferment on paying the taxes. If so, the town will wait until the property is sold for payment of the taxes, and would not start a process to sell the house to pay the taxes.
Even if that is true, however, your Aunt may still be violating the terms of the trust which require her, as the lifetime tenant, to maintain the property. If she is violating the terms of the trust, as Attorney Golden stated, she is breaching her fiduciary obligation to you and your brother to make sure the property does not lose value.
You and your brother would have to start an action against her - in court - to either force her to leave or force her to pay the taxes with her own money. Do you know why she is not paying?
To sell the property, you would need her assent because she has rights in the property for as long as she is alive. Your Aunt would probably also be entitled to a percentage of the sale proceeds if the property is sold during her lifetime.