How to subtract a negative time value (HH:MM) from a running total?

Can I assume that by asking this question that MSFT has not yet fixed the negative time bug in Excel? Have you tried simply entering your negative time (-0:50:0) and copying the formula from G12 in H12? If you are not required to be Excel compatible, other spreadsheets (LO Calc or Google Sheets) have long been able to handle negative times just fine. In LO Calc, I can simply enter my negative time in H11 (-0:50:0) and the formula in H12 is simply =G12+H11

If you must be Excel compatible, are you required to be able to read the negative value in H11? I can enter =CONVERT(-50,"mn","day") (or do the unit conversion on a hand calculator and enter the result) into H11. If the cell is formatted as time, Excel will show #######, but the underlying value is still valid, and I can still add to the previous day's running total =G12+H11. If I format the cell as general, I can see the value in H11 as decimal days.

If I want to enter decimal minutes (like in row 5), I could use a formula in row 11 to convert all of those decimal minutes values to days. =CONVERT(D5,"mn","day") [copy/paste/fill into D11:H11). H11 will still be unable to show the negative time, but I can refer to row 5 to understand what value is represented in row 11.

If it is required to be able to read row 11 as sexagessimal time, I might add a "add/subtract" toggle to row 10. I enter the positive times in row 11. Where I want to subtract the time in row 11 instead of add, I enter -1 into row 10. The formula in row 12 then becomes =C12+PRODUCT(D10:D11). With that change, I can enter -1 into H10, 0:50:0 into H11, and the formula in H12 will subtract the time as indicated.

Will any of those solutions fit into how you work with this spreadsheet?

Yes, that is the "negative time bug" that I am referring to, and I've started calling it a bug because other spreadsheets have long resolved this problem and I don't know why MSFT has not fixed this in Excel. It's really unfortunate that you must be Excel compatible, because this is a lot easier in other spreadsheets.

Yesterday's example led me to believe that the result in row 12 would always be positive. You would never subtract a value large enough to make row 12 be less than 0. In today's example, H11 is 1:45, but G12 if 1:40, resulting in -00:05 in H12, but Excel cannot display negative times in the requested sexagessimal format. In order to make these readable, we have to convert the numbers to text strings (something I generally avoid unless absolutely necessary). Here's how I would proceed:

1) First recognize that the underlying values in row 12 are correct, even when Excel cannot display them. H12 has the correct result. I would be inclined to leave row 12 alone if at all possible. You can leave the number formatting alone, or format row 12 as general so you can see the decimal days number even when the number is negative. I would also format row 10 as general, since the values in row 10 are not representing time values and you will want to be able to see the -1 values where entered.
2) In row 13, I would add a number to text formula that will provide the readable version of what is in row 12. Something like =IF(C12<0,"-","")&TEXT(ABS(C12),"[hh]:mm") in C13 and copy/paste/fill across.

The hardest part of this approach is remembering that row 13 is a dead end calculation. Row 13 is "for display only." You don't want to try to use these text strings in other calculations. If you have other calculations to perform on these times, use the value in row 12. Which is probably especially difficult if you have to communicate that to other users who will use this spreadsheet.