Your questions present several different types of options to cover your needs, but does not specify what type of needs you are concerned about. Of the 3 things mentioned, Social Security stands out as a financial aid that cannot be passed on to your family. Where group life insurance and assets from mutual funds could pay your family's bills long after you are gone, proceeds from social security typically end.
Except in the case of qualifying dependents, Social Security payments end with your demise, regardless of how much you have paid into the system. If you leave behind children or other dependents that are unable to provide for themselves, they may qualify for Social Security assistance until they are able to care for themselves or pass away, depending on the circumstances of the individual.
Group life insurance is a lower cost version of life insurance, usually sold with an upper limit of less than $500,000. The policy owner is able to name any number of beneficiaries, including people, companies, organizations, animals, places or things. Any portion of the proceeds which go to entities unable to financial serve themselves, the money be put into a trust fund that pays out the proceeds over a specified period of time. Aside from the cash value, if any, group life insurance does not provide any assistance to you and your family while you are still living.
Mutual funds are investment accounts. Investment accounts typically earn higher interest than savings accounts, and can be set up to provide you with regular income throughout your elder years, and then pay out to a named recipient after your death. Mutual funds do not have a guaranteed payout the way a life insurance policy does, but most funds allow you access to your investment and any earned interest at your personal discretion rather than tying it up until your indefinite demise.