What will happen to a roadbike when rode on broken tar?
What do you expect to happen?

Not quite sure what you mean by "roadster", but I assume it's roughly the same as a "road bike" in the US -- what would have been called a "racing bike" 30 years ago before racing bikes got all high-tech.

The main distinguishing characteristics of such bikes are that they have a more "aggressive" riding position, a lighter-weight frame, and skinny tires.  They'll also usually have "drop" handlebars, but that's true of many bikes in other categories.

All of those characteristics make it harder to ride on rough, uneven pavement, and the skinny tires can make it impossible to ride on really loose gravel.  But it's certainly possible to ride on ordinary "broken pavement", if you exercise a little care.

As to the bike, such conditions would tend to be rough on a carbon frame or exotic rims, but a bike of more ordinary construction (if you can find one anymore) should not experience extraordinary wear/fatigue.  You'd want a bike, first and foremost, with sturdy rims -- 32 spoke if possible, and at least 28.  And you should probably stay away from super-narrow tires.