I've had exactly the same problem with my Dell Vostro V131, except that, once the left-hand hinge had gone, the  right-hand one obviously had even more stress on it and followed shortly afterwards!

Once the lid broke free of the hinges, I had to manually move the hinges in order to use the laptop.  It's only then you realise how much stress is on the lid, because the hinges are almost impossible to move with my thumbs!  The hinges themselves are only about an inch long, so there's an enormous amount of stress on the tiny screws which, as you say, are screwed into plastic!!  So it's clearly a design issue.  If the hinges are required to be that stiff in order to hold the screen in whatever position you set it, then the hinges should run up the sides of the lid by several inches, to provide more torque and to enable more screws to be used, thereby reducing the stress on each screw.

I've had a conversation with Customer Support at Dell and, unsurprisingly, they won't admit that it's a design fault, because it would cost them too much to accept liability for replacing broken/detached lids ...especially since one would have the same problem with the replacements - unless they provided a metal housing (instead of plastic).  My warranty has already expired, so this is going to cost me a fair bit to resolve.  I'm not a happy bunny!  Shame on Dell for such poor design - even a child could tell these hinge fixings weren't going to last.

I work in IT and so far we had this happen to two different V131's used by different people in two different offices.

This is most definitely a design flow.  In both occurrences i have to source a whole new top lid assembly from either Amazon or ebay.  When I look at how these hinges just rip right off the plastic mold in the lid, it is obvious that this model used inferior quality plastic, in fact they should not be using plastic at all.  The XPS 13 and 14z are much better in build quality and now we learned our lesson that you get what you pay for.

The V131 is no longer made and I suppose thats a GOOD thing.  Don't touch this model with a 10 foot pole.

Another IT Admin checking in here. Multiple Vostro V131 model laptops, all of which have resided most of their life in a port replicator on a desk - not mobile. We've seen two recurring issues where the hinge itself will crack (in the same spot on the hinge in different laptops), or as OP has described, the screws pull out of the plastic backing.

Per Dell's mysterious and absolute-minded "Resolution Specialist Higher Department", "there's a indication that the parts was been physically damage".

Of course, they have nothing to back that up, including any specific action our users may have taken that would have resulted in abuse or negligence - the lid opens and closes, that's its job, and it has clearly failed for us and for others and despite our laptops being in warranty, Dell refuses to honor it.