Shichibukai are pirates who have allied themselves with the World Government. But how does it work between them? What are their rule between each other? All Shichibukai have a bounty, is that means if they got caught they still got punished? On Crocodile side, he work against the World Government, so the World Government sent him to jail. And Jinbe got jailed because he refuse to help the World Government to fight against Shirohige. But what if they didn't do anything wrong and someone able to defeat them and give them to the World Government? Are the World Government still punished them?
Shichibukai are famous pirates with large bounties who have joined with the marines. They help marines in tough situations and eliminate weak pirates. In return the World Government ignore their actions, business, etc.
As for the specific rules:
- They have to pay specific amount (1/10) of their profit to the World Government regularly.
- They will not indulge in any activity that will affect the peace of a country.
- They will have to answer the call of the marines in tough situations.
In any case if any of the above rules is broken, the contract will be dissolved and their bounty will be re-activated.
For the second question, as long as the Shichibukai has not yet broken those rules, they will remain bonded with the World Government, thus the Marines will go after the group who defeated them.
Further information can be obtained from here.
The bounties on all Shichibukai are in effect always. The World Government doesn't end the bounty on selection as Shichibukai but just avoids its implementation. The Shichibukai have to pay certain amount of their piracy earnings to WG as tax and they have to work for WG in subduing other pirates. They get caught only when
- they act against WG or WG affiliated countries (e.g. Crocodile against Alabasta);
- they don't follow WG's orders (e.g. Jimbei).
When someone defeats and hands them over to WG, they are
- put in jail, if they acted against WG (e.g. Crocodile);
- not put in jail, if they didn't act against WG (e.g. Gecko Moria).
When a Shichibukai place is vacant, WG trys to fill it asking a pirate to fill it (as they did with Jinbe). Alternatively a pirate can openly offer himself (as Blackbeard did). The new Shichibukai has to have kind of a strong reputation (this was a pre-requirement for Blackbeard).
The Shichibukai and their subordinates bounties get frozen. They get a pardon for their past crimes (e.g. Jinbe). Official protocol for WG forces are not to pursue Shichibukai, despite some marines despising them, like Smoker or Fujitora.
They are allowed to live on piracy as long as they don´t attack WG allies.
They must hand a part of their profit to WG (This rule is probably accomplished loosely due to WG not knowing all of Shichibukai activities).
They shall not act against WG nations or organizations (e.g. Crocodile). They can´t either ally another pirate crew, only add them to their own (Clearly explained at the Fujitora/Doflamingo/Law encounter at Green Bit).
They have to look strong, so they can´t afford a public defeat (as at first Moria´s defeat was not publicly known, he didn´t lose the title until the broadcasted War at Marineford).
They have to fight for WG under some circunstances not fully specified.
So if this rules are broken the Shichibukai title is revoked with all its privileges. The bounties are unfrozen (or even raised like Jinbe´s did) and they are treated mostly like any other pirate will be.