Hi Michael,
Yes, you've got the basic concept of buying a property subject to.
In that same example (seller's owe $50,000, you purchase for $150,000), the terms you create for the financing should have a balloon payment along with enough monthly to cover their mortgage and provide them some cashflow. It's normal to have terms of 3-5 years but they can be anything the parties agree to.
The hope is that in 3-5 years, you've forced appreciation on the property (rehab, value add, whatever) and the market has continued to push values upwards. Then, say, the property could be worth $200,000. At that point, you'd be able to secure long term financing through a traditional mortgage.
When securing long term financing, you'll be able to cash out 80% of ARV (in the $200,000 case, this would be $160,000). You'd get to keep the $10,000, pay off the seller's $150,000 (or whatever amount is owed at that point if some of the payments were paying down principal), and then be left with 20% equity in the property.
Hopefully that makes sense. Good luck!