Monochlorination

first Cl-Cl --> Cl^.
.
+ Cl^. --> + HCl

So the free radical formed is now planar
.
+ Cl-Cl -->
+ Cl^.

So, free radical can attack the Cl-Cl such that Cl adds above the plane or below the plane.. Resulting in a racemised product

unless the substrate is too highly strained for the free radical to be planar. remember highly strained free radicals tend to have sp³ hybridisation as in carbanions. Further there is neighboring group effects also.. In general for simple compounds monochlorination usually leads to a racemised product

free radical formed is sp2 hybridised and hence is planar.
the attack of cl free radical can take place fron either side of plane .
hence racemoc mix is formed.