If a paper contract is signed between 2 parties, each consisting of 2 people, and one individual does not sign, is the contract still legal?"

The answer depends on many factors, including: Was the contract of a type which is required to be in writing (most are not), or did the parties contemplate that their agreement would not be enforceable until it was reduced to writing and signed by all parties? Is the contract of a type which needed all 4 people, or could it be performed with only the three who signed? Did any of the signatories have authority, or apparent or implied authority, to bind the non-signatory? Did the non-signatory subsequently ratify the agreement, either expressly or by conduct? Did the parties perform, in whole or part, under the agreement? Moreover, the answers to some of these questions may not be clear cut, or may be the subject of dispute.  For example, one side may say "we had a verbal agreement" while the other may say "we all intended that the agreement would not be valid until everyone signed".  Bottom line is that the answer is not clear, at least based on the facts contained in your question.