So my ending capital account balance on the return will be zero as will all other balance sheet accounts (though those aren't shown on the account).
That is correct - after all remaining assets are distributed - the ending balance should be zero.
How do I show that I have a personal liability and now if I am responsible for paying debt that will not be discharged through the bankruptcy, I get not tax benefit from that?
You do not need specifically "show" you personal liability - all assets and debts are passed to you on K-1.
Because of eliminating all the other payables, I show net income. If the payables were shown as adjustments to capital instead of income, wouldn't I be better served because I would show a loss?
If payable may not be collected - that is a bad debt and is written off and deducted (if previously was included into income). If that resulted a business loss - it is passed to partners on K-1.
And if the actual discharge occurred after the closing of the business if we are saying a shortened year, can I not show it as income?
Yes - if the account payable is distributed to you from the partnership - that is your income when collected.
It justs doesn't seem to make sense that I am personally responsible for this debt, lost money in the company and then am still going to owe taxes.
A partnership is the relationship existing between two or more persons who join to carry on a trade or business. A partnership must file an annual information return to report the income, deductions, gains, losses, etc., from its operations, but it does not pay income tax. Instead, it "passes through" any profits or losses to its partners.
So - whatever business losses the partnership has - these losses are passes to partners.