Will the magnetic field still remain if there is no current in the electromagnet? Why Will the magnetic field still remain if there is no current in the electromagnet
 A: There are two ways of having electromagnets, as seen in the introduction here.
a)

An electromagnet is a type of magnet in which the magnetic field is produced by an electric current. Electromagnets usually consist of wire wound into a coil. A current through the wire creates a magnetic field which is concentrated in the hole, denoting the center of the coil. The magnetic field disappears when the current is turned off.

That is one kind of electromagnet. Or:
b)

The wire turns are often wound around a magnetic core made from a ferromagnetic or ferrimagnetic material such as iron; the magnetic core concentrates the magnetic flux and makes a more powerful magnet. 

Ferromagnetic materials retain an imposed magnetic field, so for these electromagnets there will be a remainder field even if the power is turned off.
A: Faraday's laws of induction states that for a change in current in one conductor there is a proportional change in magnetic flux induced by it.
In your case as the conductor has no current for long time hence leading to inference that change in current is zero so there will be no induced magnetic field.
Hence the electromagnetic loses it's magnetic strength.

But coming to a realistic world does it always happen?
No
Your magnetic flux carrier material is made of ferrous materials hence it has prominent dipoles. In case the carrier has the magnetic field for a long time the dipoles will align and hence give the material a permanent/temporary magnetic characteristic, making it essentially a powerful magnet.
And this is also a major reason why choice of material is necessary while building electromagnets.
Higher retentivity leads to higher residual magnetic character in the material even after the current is cut off.
A: No, I mean it will remain still at zero, but that's not what you're asking I guess.
For a material to maintain magnetic moment, which is the only possible way you can generate static magnetic fields, it needs to be properly magnetized. There are only certain materials that can be made into magnets (see here), and the conditions for which they will become permanent magnets probably will not occur in a electromagnet.
So, no, the magnetic field does not remain in the electromagnet after the current is cut, because there is nothing that will continue to provide magnetic field.
