What would most likely happen to a unicellular organism if it was exposed to a hypotonic solution for an extended period of time?

The answer is that a unicellular organism would swell and burst.

In a hypotonic solution the water concentration of the cell's cytoplasm is lower then that of the hypotonic solution. If unicellular organism is exposed to a hypotonic solution, the water from the solution will enter the organism by the process called osmosis. The aim is to balance water concentration on the inside and outside of the organism. But, that water entering the cytoplasm of the cell will make pressure on the cell membrane. If the excess water cannot be removed from the organism, it will swell and burst.