Pretty easy. In fact it's a great noob first repair to get started on learning about what makes a bass "tick".
That is the output jack. In fact, it's a barrel type jack (long tube) which are known for not lasting very long and needing replacement regularly. It really hasn't anything to do with the cheapness of the bass as quite a few basses of all prices use them sometimes (Carvin). It's really about the style of jack. Putting in a different style is a huge hassle and replacing it is easy so that's the common fix.
1. You buy a new barrel type jack either online or at local guitar store.
2. If you don't already have a cheap soldering pencil get one at radio shack or local harware store. You don't want a huge "iron" just a "pencil". They are in the heat range of about 30 watts or so. Cost about ten bucks or less.
3. Get some electronic rosin core solder. You DO NOT want acid core or acid flux designed for plumbing. it will corrode your bass and do damage. Usually the places that have the pencils also will have the electronic solder.
4. Clip the wires off the old jack noting how they were connected although new jack may be different. Then bolt in new jack.
5. final operation is to carefully strip back the wire and resolder to new jack terminals. This is the tricky part. Your bass is passive so you'll only have to worry about two terminals, but the jack will probably have three. The wire going to the jack appears to be shielded cable (that is good) so the two connections will be to the center wire for "hot" and the shielding which will be braid or multiple wires wrapped around the center wire under the plastic covering. That will be the "ground" connection.
6. Figuring out the terminals on a barrel jack can sometimes be a trick if it came with no diagrams. Basically one of the two or three terminals on the end of it will be attached to the outter "barrel". That is the "ground" and it's where the wire shield will be soldered. Finding the hot terminal takes a trick. Plug in your amp to the bass new jack. Keeping volume low, take your finger and touch each of the terminals on the jack. One of them should make the amp hum like mad. THAT one is where the "Hot" wire from the volume control goes. The third terminal is a swtich for the battery in an active bass and you don't have to worry about that. You could short it to ground, but its not necessary.
7. At that point you just put the bare wire through the hole in the terminal and wrap it around and flow solder on. (not too much). There are lots of "how to solder" videos on line if you are scared about this part.
Hey, if I could learn to use a steam iron to take the old fretboard off my SX bass successfully, anybody ought to be able to solder a couple of terminals after watching Youtube!
And having done it once, next time that jack goes West, you'll be ready!