THe purpose of campden tabs is to provide s02 (sulphites) that stuns or kills wild yeasts so that your wine yeasts can get first crack the sugars in your must. If your making wine from fresh fruit or grapes, then you definately should consider sulphiting your must.
Most wine kits include a packet of potassium metabisulphite that is added after fermrntation is complete and before you start the degassing or racking procedures. Sulphites are a thing that will dissipate out of wine over time through the airlock.
I've found that wines with more sulphites are more likely to cause a bad hangover. Thats why i try to leave them out whenever i can.
The sorbates (stabilizers) are chemicals used to kill off all the yeast once they are finished converting the sugars into alcohol. They are also used in a wide variety of food and pharmacy products as preservatives. While they will prevent renewed fermentation, they will not stop an active one.
(I have read that Potassium Sorbate is prescribed as a cure for feminine yeast infections

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If your wine is clear and the SG has been stable below 1.000 for at least a month, then you dont need to stabilize. There shouldnt be any sugars left to wake your yeast up. Just be extra careful with your cleanliness and sanitation.