The wing of a GA airplane is designed so that the root of the wing (i.e. the part of the wing close to the fuselage) stalls before the wing's tips. These has mainly two positive effects:
1. when the root stalls, its turbulent wake impinges on the tailplane shaking it and warning the pilot of the incipient stall;
2. the outer part of the wing keeps on lifting and the ailerons keep on working.

Anyway to answer the question at least two other phenomenon should be taken into account:

3. in normal flight (i.e. not at stall) the airflow seen by the horizontal stabiliser differs from the one seen by the wing due to the downwash of the wing which decreases the AoA of the horizontal stabiliser. That means that the horizontal stabiliser has to be set to a higher AoA than if it were isolated;
4. we are all well aware of lift and drag coefficients (at the end of this answer I posted the plots of $C_l$ and $C_d$ for a classical airfoil like the NACA 2412, used for example for the wing of the [Cessna 172][1]). Anyway lift and drag do not tell the whole story: to completely describe the aerodynamic characteristics, a third plot is needed, which is as important as the other two but which is normally ignored: the plot of the *pitching moment*. For the same NACA 2412 it looks something like that (underlined in green):
[![ pitching moment coefficient NACA 2412][4]][4]
What does this plot tell us? The pitching moment is normally negative i.e. nose-down. And that's why the horizontal stabiliser has to normally produce a downward lift i.e. a nose-up moment. But what happen at stall? As soon as the stall region is reached (at some 16°), the wing's pitching moment becomes suddenly almost five time more negative than just before the stall. This drop in $C_m$ sums up to a sudden drop in $C_l$ and rise in $C_d$.

Now that we have all the needed ingredients, understanding what happen approaching stall is quite easy. So, the root of the wing stalls and basically two main things happen:
* a) pitching-down moment of the wing's root increases as explained in 4.;
* b) the stalled wake from the wing impinges on the horizontal stabiliser shaking it as in 1. and, above all, this stalled wake doesn't generate downwash anymore as defined in 3.

The consequence of a) is that the stalled wing makes the aircraft pitch down; while the consequence of b) is that the AoA of the horizontal stabiliser increases, which lowers its downward lift, which makes the tail go up i.e. the aircraft pitch down. So, the main result of a stalled (root of the) wing is a pitch nose-down tendency.

If no corrective measures are taken, other effects follow:
1. lift drops... and the airplane as well;
2. drag rises; if the stall was entered because of a too slow velocity, higher drag will slow the airplane even more down.

Point 1. is actually not that bad as it might sound since it has two positive effects:
* the fact that the airplane falls down makes it gain speed again, counteracting the drag increase of 2;
* the horizontal stabiliser is (should be) designed to stall well after the wing so it is still producing lift and since the aircraft is falling down, the local AoA seen by the horizontal stabiliser increases again compensating for the decrease due to the loss of downwash as explained in b).

***

Here under the plot of $C_l$ (underlined in blue) and $C_d$ (in red).

[![ lift coefficient NACA 2412][2]][2]
[![ drag coefficient NACA 2412][3]][3]


  [1]: https://en.m.wikipedia.org/wiki/Cessna_172
  [2]: https://i.sstatic.net/Q3794.jpg
  [3]: https://i.sstatic.net/oSkwg.jpg
  [4]: https://i.sstatic.net/ypPC3.jpg