Actually there are some non-MSTP programs that are non-funded or partially funded. Here are my personal definitions on various program types.
Non-funded programs are ones that provide nothing towards your medical school, but are integrated in that you can still get your PhD in between the second and third years of medical school and get the usual stipend and tuition remissions during your graduate school years.
Partially-funded programs are ones that provide funding only for your graduate school years and last 2 years of medical school. In this case you have to foot the bill for the first two years.
Some other programs (a shrinking number) are competitively-funded. In this case, some students get funding and some students do not. Sometimes you have to fight for your funding during the program or in other cases that decision is made permanent before you matriculate into the program.
Most MD/PhD programs, including all MSTPs, are fully-funded, in that they give tuition remissions and stipend for all years of study. In this case, you should expect to graduate from medical school without debt. Nevertheless, at some programs you do have the option of taking out interest-free (through residency) stafford subsidized loans that could give you a small amount of debt-load. No DO/PhD programs are fully-funded, while some are partially funded and others are non-funded. For a program to be competitive for the MSTP grant, they need to have a well established fully-funded program. For this reason, do not expect a program that is not fully-funded now to get the government money.