What happens when a pilot has no Instrument Rating and visibility drops?
It is very rare for weather to go IMC unexpectedly.

A responsible pilot should see that weather is deteriorating, and begin planning for the nearest available landing.   If they cannot find a landing, they should contact ATC while still in VMC, declare an emergency, and begin working with ATC to get down safely.

In some cases, a pilot may inadvertently enter IMC unexpectedly.   The standard procedure is to execute a standard rate 180&deg; turn, and fly equal time in the opposite direction.  That should get them back to VMC conditions. 

If that doesn't work, unfortunately inadvertent flight into IMC is a leading cause of GA accidents, especially CFIT (Controlled Flight into Terrain - i.e. 'aircraft flew into the ground').   Because of that, even basic private pilot training includes more basic instructions on instrument flying (BAI) than it used to.