Unfortunately, without paying the arrears, I'm not aware of any other out. You should look up your state's right of redemption laws which tell you how long you have to pay arrears to get the property back. For unpaid dues and special assessments, the HOA can lien and foreclose even if you have a live mortgage on your condo that you are paying on time. Contact the HOA attorney and see if they're interested in entering into a payment plan with you.
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You need a lawyer, and, even more, you need a realtor specializing in distressed property. You can either let the sale happen and hope that it gets stalled for one or another foreclosure moratorium, or you can get out in front of this thing, list and sell the condo, use the profits to pay your rent, and re-enter the market when you are through the crisis. The first approach will surely destroy your credit rating, making a re-entry much more difficult. I have no idea whether the condo is valuable enough to sell for an adequate price before the couple weeks left before the auction, but a lawyer might negotiate with the condo HOA to a reasonable result. Besides, the DC market is quite hot again. Indeed, it is also possible that a lawyer could refer you to an investor specializing in distressed situations who would buy the condo HOA lien so that you could sell to them. But, sitting on your options is unlikely to make this better.
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