You have a contract to buy the house for a specific amount. That amount applies, regardless of any debts or liens on the property. However, the seller has to have clear title, and that isn't possible if there's an outstanding lien. If the owner really is "broke," presumably having no money to pay off the lien, that would normally be done at closing, out of the amount you're paying to the seller.
Let's suppose the seller owes $10,000 in debt and there's the $15,000 lien. We don't have to worry about the debt; that won't affect the sale. Suppose you're buying the house for $215,000. Typically (after commissions, other expenses, etc., which we won't deal with here), $15,000 of your purchase money would be used to clear the lien, and the seller would receive $200,000...minus commission, expenses, etc.
However, suppose there's a $215,000 mortgage on the property (a mortgage is a lien). Your $215,000 purchase proceeds would retire the $215,000 mortgage, leaving the seller with a sold property but no funds.
Now suppose there's a $215,000 mortgage plus that $15,000 lien. You pay $215,000 for the property. The seller owes $230,000. The seller would have to bring $15,000 to closing. And if the seller is broke, then the seller can't afford to do so.
That's probably why your agent was suggesting you pay $15,000 more. But your analysis is 100% correct. You'd be paying off her $15,000 debt in your mortgage for the next 30 years. Now, using the numbers above, if you'd be paying $230,000 but the house is really worth $400,000 in today's market, that would be a good deal...a deal worth doing. On the other hand, if $215,000 is the current fair market value of the property, it'd make no sense to overpay by $15,000. In fact, the house might not even appraise for $230,000. So, from an investment standpoint, you have to ask: If I pay $15,000 more, is it still a good deal? If yes, then maybe you ought to at least consider going ahead. If not, then consult with a lawyer on how to get out of the transaction.
Decreasing your offer by $15,000 doesn't make sense from a mathematical perspective. It's a good negotiating technique if there's equity in the property, though, and you just want a better deal. Again, though, make sure it's done with a lawyer's approval.
If it were me, I'd try sticking to the negotiated, contracted price. Only if it's an absolute bargain--such a bargain that even paying up to $15,000 more (and you might not have to go up to the full $15,000) would still keep it a bargain--would I consider paying more.
Hope that helps.