its plasticizer. Most figures that contain mostly PVC will tend to leak out plasticizer.
Poly Vinyl Chloride (PVC)
PVC is one of the most common plastics used in the world. It's quite similar to rubber and the toughness/malleability of PVC is dependant on the plastisers added. More plastisers = more softness, since they straighten out neatly the long macromolecular polymer chains into neat rows. Some figure collectors complain of an oily film after a while and I would think this is due to the plasticisers migrating to the surface of the plastic. Small plasticiser molecules are pretty mobile and after a period of time, they accumulate on the surface to produce a oily crud.
This is also why PVC tends to get a bit crappy and brittle after a long time. Oh yeah these plasticisers are quite toxic too. And if you have a fire at home, dump your figurines at them to extinguish it, since the chlorine produced retards the flame. Btw, some plasticisers are thought to reduce the quality of MAN SPERM.
A very large percentage of the figures sold are made of PVC. From gashapon, trading figures to 1/6s, these are mainly PVCs. Cheap material cost, easy of moulding, ductility (it won't break much, just bend) are the reasons why it is used.
Never leave them in the sun. Ultraviolet rays produce free radicals on PVC, chlorine free radicals, that combine to form chlorine gas and the material is decomposed. The sun also heats them up and PVC distorts at a temperature of 60 degrees Celsius. Being a thermoplastic, you can actually heat it up and bend it, then cool for it to maintain that shape.
PVC, due to the addition of chlorine atoms which have a pretty high molecular mass compared to C and H, is heavy for a plastic.