First you have broken socket on a figure. 

In this case this is someone else's figure, so I won't be able to fix this figure, but I will show you how to fix it. 

Bend the rod 90 deg.

Have it just as long as the socket is (Leave the excess)

Check the Impression; make sure it looks good
Lightly press the sides of the mold (the Play-doh) to shrink the mold size.

Don't fill it too full

Remove the cooled hot glue from the Play-doh.
You may have to wash it off under with water.

Press it into the hot glue

Check it with an arm to see if it works

(Just bend the end of it.)

Push the good socket into the Play-doh

Add hot glue to the mold

Put mold and hot glue in the freezer for about 10 minutes

Heat up the metal rod on the short bent end with a candle.

Bend the wire to match the inside contour of the broken figure.

Add more hot glue to the rod

Fill the figure with hot glue and lay him on his side (Don't add too much, just enough to fill past the rod when put into the hole)

Slide new socket and rod into open hole in your broken figure. Touch up with hot glue, let cool - done.