We took down my daughters light to replace it and there is no metal junction box in celing.. Just wires.. Is this dangerous to have no plastic or metal junction box to house the wiring in the celing?.

How old is this house? Can see tell us what the wires look like and if they are a cable or in conduit orwhat. Do not install that light until we walk through this, yes it can be dangerous.

Not only dangerous but against code. For a VERY light luminaire you may get away with an old work box but by code, a fixture rated box must be attached to a building member. Can you get above area?

Yes it is.

Circuit needs to be turned off and the wire put into a box.

Is the wire covering plastic, or woven fabric looking stuff? (cambric)