You can have negative work just like you have negative acceleration.
Negative work is just the removal of energy from a system, where positive work is adding energy to a system.
One example of this is block dropping with an attached spring. The string is generating an upwards force on the block, but the blocks displacement is downwards.
W = F dot s =|F|*|s|*cos(theta)
In this case, theta is pi (or -pi) radians. cos(pi) = cos(-pi) = -1. Since the magnitudes of F and s MUST be positive (magnitudes are always positive) this implies that the work done is negative.
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