Okay so there are many kind of antibodies - IgG, IgM, IgA and IgE.

IgA are only functional outside of the body (in your intestines and in your respiratory tract). IgE are only functional once bound to a very specific type of cell - they cause allergies. IgG and IgM, on the other hand, have many purposes. Which…are complicated. You have something floating around in your blood called complement. When Complement lands on something, it tells your immune system to kill whatever it lands on. So your body only wants complement to land on diseases. One of the ways it gets it to do this is by haveing antibodies (IgG and IgM antibodies) make complement settle onto diseases. In this case it isn’t really gobbled up - it makes proteins form that literally punch holes in pathogens (and ramp up your immune system so any survivors can get gobbled up).

The other thing it can do it make you immune cells gobble up whatever it binds too so it can kinda do both!

Antibodies are made by the immune system, specifically B-cells. They are used as targeting proteins so that your body can respond to diseases/pathogens. If they are expressed on the surface of the B-cell, then when they find and bind to something 'foreign', they can then cause the B-cell to proliferate (divide and multiply), meaning that your body can fight off the disease. They can also be secreted from other types of B-cells (plasma cells) which flat around to monitor your body, and then bind to foreign pathogens and act as a flag/beacon for other immune cells to come and investigate and attack (T-cells/NK cells).

In terms of what happens when they're not needed, the cell surface expressed antibodies will stay around as long as the individual cell lives (the cell probably recycles and makes more to put on the surface over it's lifespan) and the secreted antibodies will degrade over time or be processed and degraded by other immune cells. The plasma cells will tick over and are there to make more if the disease invades again.