What property of metals allows them to be shaped into wires?

Ductility

Explanation:

Ductility is the ability of a metal to be converted into a thin wire without getting break and loosing its hardness. The property of Ductility of a metal allows us to make a wider use of them. Some most ductile metals are gold, silver, copper etc. whereas some of the metals with very less ductility are tungsten, steel and other alloys as they are very hard to transform into a thin wire.

A metal with less ductility can be malleable as it can have the ability to be converted into a thin sheet. Not all the metals are ductile but some of them have high ductility, some have less and some of them are non ductile.