spice simulation single supply opamp

I am simulating a single supply opamp in an inverting opamp configuration with gain set to 1. I/P is an ac sine 200mVpp 0Voffset. I am using the TLC081 TI single supply opamp spice model. Qn) When input sine wave becomes +ve wrt gnd , then o/p should drive negative. Of course that can't happen because we have a single supply system. In the simulation i see an o/p DC offset(300mV) wrt which the o/p sine wave swings up and down. Does this mean that in a single supply opamp the o/p always gets a DC offset even if input has no DC in it? I don't qualatatively understand what happens when V- input of a single supply opamp crosses the V+ input(0V always in this case). Thanks