A enclosure assembly with a support for a mattress of a bed to accommodate a person on the mattress, the enclosure assembly including a framework having connectors to secure the framework in an upstanding relation peripherally about the mattress, the framework including corner posts each extending a generally common distance above the mattress, and frame members spanning the corner posts. A net having inside and outside surfaces is supported on the framework and has at least one normally closed opening provided with a closure member which may only be opened from the outside of the net, thereby at least partially defining a "safe zone" about the periphery of the mattress. The enclosure assembly also comprises a coverlet which overlies the mattress and is removably interconnected along its periphery to the inside surface of the net, thereby further defining the "safe zone" about the mattress on which the person may rest without risk of falling off the mattress and harming themselves.