What happens if a family of 4 only shows 3 people on their apartment lease?

We are a family of 4 adults and currently we are searching for an apartment. 3 people are working and our income is becoming too high to be considered for an apartment. But when we are looking for non income restricted aparments, we cannot afford to pay the rent. So my question is whether we can hide one person on our apartment without their name on the lease. If so, what can be the consequences???? Thanks in advance.

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