KE cannot be negative, but the KE term in an equation can have a negative sign.
For example, in PE = KE (potential energy equals kinetic energy), we can write PE - KE = 0 But that does not mean the kinetic energy is negative, it just means that all the potential energy is converted into kinetic energy so that there is no more energy to expend...it's all spent.
As many have pointed out, KE = 1/2 m v^2; so even if v<0, the square causes the KE to remain positive. Think of PE as sand in a hopper; it stays there until we open the stopcock. Then the sand tumbles out of the hopper and that represents kinetic energy because the sand is moving.
But the sand in the hopper, which is the potential energy, is being used up as the falling sand continues until all the sand in the hopper is gone. PE - KE = 0 indicates the end game when all the sand (potential energy) is used up.
Physics and engineering degrees.