So the problem is whenever I plug my headphones into the amplifier, I can hear the sound amplified but if I unplugged the headphones, the amplifier does not release any sound. What could be the cause of this?
Sounds like the headphone socket switch has been wired wrong: it usually is responsible for switching the amplified sound off when the headphone is plugged in.
However, that sounds like something that cannot happen without intention, or at least without the one soldering the headphone socket in noticing.
So are you sure this is a headphone socket? Is it labelled as such? Does it behave in other respects like one (for example, following the volume setting)? Is that a stereo or a mono headphone (the plugs are somewhat different, and if you are using a non-headphone socket, the reactions may differ)? Are you using some kind of headphone adapter for plugging it in?
I am assuming that if you write "I can head the sound amplified" you mean that the amplifier is producing sound through its normal loudspeakers as well as the headphones.
In any case, your situation is unusual and so it would be quite important that you describe very accurately what output you hear through what devices with exactly which plugs and adapters in which socket labelled as what in which situation.
Only then will it be possible to figure out what is different from how it is intended to be.
For example, if you put a headphone into a socket for a footswitch (reverb on/off for example), it's anyone's bet what will happen.