Keeping your paycheck and imagining that you have to pay the damages is illegal. You do have a verbal contract for services to care for the elderly couple, which is a valid contract, and as you say, that contract did not contain details about your responsibility for damage to property; and responsibility for that property can't be assumed to be in the contract as an after thought by the other party, the landlord. But do you have anything in writing? Letters about the job when you first started? Emails? Phone conversations you remember? Gather those materials and write down what you remember.
You do need to find legal help. Try contacting Montana Legal Services Association (MLSA). They offer free and low cost legal help. They can help you with options to take and how to respond to the landlord's demands. If they can help you respond to the landlord/lawyer, the fact that you have talked with MLSA will show the landlord/attorney you have been getting legal advice, and could defuse the situation. The landlord's motivation may simply to try and take advantage of you, and the pushback involved with you talking to MLSA could result in them backing off.
Another option is to talk to a lawyer in your town; find one who advertises free initial consultations. I assume you're not going to be able to pay much, if anything, but you may find a lawyer who would pick up the phone or write a short letter for free (pro bono) in order to help you out. Even if the lawyer doesn't specialize in contracts, they may help. If the landlord/attorney is contacted by a lawyer who is helping you, that will show them you're serious about defending yourself.
Don't ignore the letter or the situation; that will make worse the legal situation you've been thrown into. Unfortunately, people like the landlord/attorney like to break contracts and intimidate people into monetary settlements when they're unhappy with a situation. So find some legal help and defend yourself.