The answer is no!
We recommend clients have gifts and distributions impact units. When new gifts come in, units are bought at the current unit price. When a distribution occurs, units are sold. Earnings will increase unit price and losses will decrease unit price. As the unit price/market value of the fund increases the number of units sold each period will decrease. If unit price decreases (such as in a loss scenario) units distributed will increase (inverse relationship between unit price and units).
Below is a history report of a fund that has distributions sell units. In each instance of a distribution, fewer units are sold. Assuming your pool will continue to grow, the unit price will continually increase, and the number of units sold for distributions will continually decrease month after month, year after year. It will be impossible for the units to ever be zero or negative as unit price and units is a proportionate calculation.
Even in an instance where a fund is no longer receiving gifts, the same logic holds true. The number of units sold each time will decrease, the fund will not run out of units even if no new gifts are coming in.