It depends on what you mean by "liability"
I presume by the context your question that you mean "could I be responsible for obtaining permits for the work completed?" In that case the answer is no. Whoever did the work was responsible for obtaining permits.
If you meant "could I be potentially legally responsible for possible damage done by faulty work? (i.e. poorly done roof, electrical, or plumbing?)" In that case the answer is maybe. There's some release of liability in the fact that they disclosed that the work was not permitted, but you bought it anyway, but that doesn't exonerate them from negligence. The fine line there is usually drawn by lawyers and insurance companies.
If you meant "is it a negative impact on the value of the home that I am assuming?" The answer is obviously yes. When you sell the home you'll have to disclose the unpermitted work as well, which hurts the value. The bright side for you as a buyer is that it can be used as a negotiating tool. Depending on the county and the individual inspector(s) you get, you may be able to permit unpermitted work permitted, but there's risk involved. If the work done was not to code, it will have to be brought to code to be permitted. Even if it was done to code, you may have to hire a contractor to give inspectors access to places like inside the walls, or hire an engineer to inspect and sign off on the improvements. For those reasons it's usually not worth getting old work permitted that wasn't initially permitted.
My advice would be to seek credentials from the seller for the work that was done, or get a professional home inspection. If the improvements were made by a reputable contractor that avoided the additional costs of permits, it's probably worth the investment, and you can include those credentials in your disclosure of you ever sell the house. (i.e. such and such was unpermitted, but done by licensed contractor this and that)... or, (i.e. such and such is unpermitted, but this and that inspected the work and said it looks good). Those options are the next best things to permitted work when reselling your house, and don't cost an arm and a leg. Plus, they give you peace of mind that your house won't burn down in your sleep because of faulty work... which is why they mitigate some of the loss of value of doing work without permits.