This would probably last forever. The MD class size is only around 120 people and at 70k per year tuition costs would be 8.4M per year (ignoring that only families earning under 300k are eligible). Modest interest on 1B would easily earn over 10M per year and probably several times that. Hedge funds often manage these endowment funds.

Only until some clever people figure out how to attach themselves to the money and suck the whole thing dry in few years.

Ah the essence of capitalism. Leeching middle men

Until $1B runs out? Tuition is like $70k per year, so $1B should be enough to cover 3300 students for four years.

University endowments are usually used the way kwkelly has (since you commented) explained [*] - investing it and using the returns, rather than burning through the capital until it's all gone. It would be extremely surprising in this case if they chose to do it the way you're thinking.

[*] https://news.ycombinator.com/item?id=40925597