Would socialism stop companies from moving jobs overseas?

that's the idea, yes. If workers own their factory and enjoy the profits, they won't move production abroad and make themselves unemployed.

However, the Mondragon corporation does invest in foreign countries

It may work.  But there is a caveat.  If someone else can set up a factory elsewhere and create things more cheaply then the local company tends to go bankrupt.  You can have a level of protectionism to counter this.  But that leads to a lower standard of living for others so they would vote against it.  No one seems to realize that a nation is like a boat.  If everyone keeps drilling holes through the bottom you ALL sink.

Soon the government will be taking over businesses so they can pay all the illegals and thugs to work for them

People are fleeing in droves from socialist Venezuela

Social Security, Medicare, public roads, bridges, and Libraries are forms of "Socialism".