We the People of the United States, in Order to form a more perfect Union, establish Justice, insure domestic Tranquility, provide for the common defense, promote the general Welfare, and secure the Blessings of Liberty to ourselves and our Posterity, do ordain and establish this Constitution for the United States of America.
General welfare not individual welfare. This means we should provide an environment where success is available to all rather than guaranteeing success to all. A safety net could be intended but likely wasn't because it is juxtaposed to the liberty clauses. Liberty means freedom to succeed and freedom to fail.