Yes, they can, but it is unlikely they will. Their lien survived your bankruptcy, although by not reaffirming the debt your discharge means you are not personally liable on the debt. If he second forecloses, it would lead to a sheriff's sale, where the first mortgage holder will be bidding the full amount owed to them. The second would have to bid higher, pay off the first in full with hard cold cash, and then try to sell the house for at least more than the first mortgage bid. Foreclosed homes tend to sell for 60-80% of fair market value. So, yes they can foreclose, but they might be bluffing, which in turn may be fair debt collection act violation.
Your options include, to realize this is likely a collection attempt, without a real intent to proceed by the second lien lender, as described by my colleague.
The existing county appraisal may be influencing this collection attempt, because the valuation indicates there is available equity towards liquidation of a portion of the second lien.
You may benefit from protesting the value of the property, to lower the valuation closer to what you believe it could be sold for.
This will likely remove any incentive to market the property by the second lien holder, unless they have secured a buyer already, in which event you may have to move, if foreclosed upon.
General legal advice is offered for educational purposes only. A consultation with a qualified attorney is required to determine specific legal advice as to your situation and applicable law. We are a debt relief agency and we help people file for relief under the bankruptcy laws.
Although the 2nd mortgage can foreclose, there is no profit for them to do so. I would hope you can set money aside each month to try to settle this matter for a lump sum of cash. To accomplish this, I would obtain a certified appraisal supporting your claim of value. You may want to wait until the 2nd mortgage is sold to a debt collector before making an offer to settle. Hope this perspective helps!