Can faulty headset be fixed?

Many audio and electronics shops will do headphone repairs. If you can't find a local place to do the work, you can look into shipping your headphones to the manufacturer or an independent repair center for a fix. And depending on the problem, your headphones may be covered by a warranty as well.

No, I have no knowledge about this mater.

If it is just electrical as others commented, and not that you went swimming with them, yes.  9 times out of 10 its the plug end.  To verify the plug end is all that is wrong will require you to test the headset after you remove the old plug.  Of course, you used to go to Radio Shack and find the plug you needed, but you also had to be able to solder without melting everything.  Amazon will have them, be sure of the diameter and stereo or mono. You would have to cut the old plug off, it is all molded together and unusable, trim and tin the wires, and they are very small strands that are hard to remove the insulation from without ripping the wire too, and solder the wires to the new plug.  If they are a Walmart special, buy new, a high end expensive set, try and fix them. Assuming you have no ohm meter to test it, which you can get at Harbor Freight for 6 bucks, with all the wires separated, if stereo you will have a center wire and a shield for each ear piece, put the headset on your head near, not on your ears, use a regular battery like out of one of your remotes, hold one wire on one battery terminal, and very quickly just brush, don't hold contact,  the other wire across the other battery terminal and listen for a click in the headset ear piece, do this for the other one too.  If both click, you just need a plug.

If you really want them fixed and don't want to do it yourself, do not go to an electrician for this work.  A TV repair shop will probably do it for a few bucks if you bring them a new connector, if you can find the connector, and a TV repair shop. Some independent computer repair places should also have the skill needed to do this too.

Maybe, unless you do it yourself it isn't economical.  

It depends on the type of fault. Usually the damage is a shorted or broken wire, which can be spliced or resoldered. A burned-out headphone cannot be repaired. A water damaged headphone cannot be repaired.

no replace them , to fix them its costs to much , just buy another pair , 

todays  headsets always are assemble on the cheap,high mark up,with teeny components and mousewhisker wires that break after a few weeks of use, walgreens earbuds cost ( a few years ago they were like seven bucks) 15 bucks,last maybe a year  toss them n buy another,,old headphones from the 80s and 70s are out there,most former owners are in old folks home, the headphones are starting to get to the same stage

Most headphones break simply due to wiring being pulled out or the soldering disconnecting. As one user said, yes it can be done... but only worth it if you do it your self. Headphones are actually very simple electronics. Most of the time its the wire that gets disconnected only has two solder points, and you can open the connection up and just solder back on the connection that came lose. its actually really straight forward and only takes a few  minutes to do. However, paying a repair service to do that for you would probably cost as must (if not more) than the head phones.  

I had a broken earphone from the airline. I opened and soldered the wire back onto the speaker. It worked a few months.

It can be, but unless you do it yourself it isn't economical.