You are 50% partner in a general partnership. the business has outstanding debts of $250,000 and is closing due to the death of your only partner. what is your personal liability?

Laws vary by region, but if you had a general partnership with no clause accounting for the death of the partner, you may have to liquidate the company, and will owe the estate of your deceased partner 50% of the net value. If the company has greater debts than assets, you will take on 50% of that remaining debt after liquidation. 
If you take over the company, as agreed with your partner prior to his death, you will be the 100% owner of the company, and thus your liability to the 250,000 will be 100% of that amount. You would have the option to find a new partner. 
Another possibility is that the partner selects a mutually agreed heir to his interest in the company, such as a spouse or business associate, in the event of his passing. This would leave you with the same interest in the company, and thus the same 50% liability to outstanding debts.