Polymers have a special property called viscoelasticity, which means they may strain elastically (elasticity) then flow (visco). The models below are mechanical representations of this phenomenon using springs and dashpots (dampers).
$\qquad\qquad\qquad$ Maxwell Model $\qquad\qquad\qquad\qquad\qquad\qquad$ Kelvin–Voigt Model
$\qquad\qquad\qquad$Time Stress Deformation Plot
This property of viscoelasticity allows plastics, when pulled slowly (low strain rate), time for the polymer chains to rearrange and the plastic to flow which means it is less rigid but more elastic (think stretching silly putty). When the plastic is pulled quickly the plastic is more rigid and breaks (like breaking silly putty). AS I have alluded you can observe this with silly putty which flows when strain is low and will stretch to long lengths while snap into two pieces when pulled rapidly.
So far I have only explained why plastics will stretch or snap, but not why they are hard to tear after stretching. This is caused because as the plastic is stretched the polymer chains align as shown below. As it turns out polymers are hardest to tear perpendicular to the direction of the molecules because you have to break the bonds of the chain rather than some bond breaking and some chains separating. As a result, the plastic becomes hard to tear across the stretched part, but it is now easier to tear along the stretch (parallel) since in is mostly chain separating to do so, and indeed a tear in a stretched bag will follow the direction of a stretch.