If you're strictly following game rules, then the player is not eliminated, they have still amassed some points, maybe enough to win.
You could automatically play for them, but again maybe they want to choose the Transport action to influence the coal placement.
There is the wage action and the Inn, but maybe you have not yet accomplished those developments.
For a new rule idea, you could:
1. Lewis & Clark style, reset everything.
2. Forgo a turn to gain 2 Thalers.
3. If there are no debts left, then trade 2 VP's for 2 Thalers.
4. Eliminate the player.
5. Trade development cubes for Thalers.