On a low level there are no "coins", just numeric amounts of smallest units of Bitcoin (satoshis) attached to outputs. Outputs have predicates (scripts) that al

On a low level there are no "coins", just numeric amounts of smallest units of Bitcoin (satoshis) attached to outputs. Outputs have predicates (scripts) that allow the one who can satisfy the predicate to move amount in the output. Generally it's EC signature requirement but can be more complex. A transaction has also inputs that indicate which output do you want to claim and some data that satisfies the predicate (generally it's also a script but usually only data). And yes, it's not possible to hide stolen Bitcoin. These addresses will be monitored forever. Think about what would happen if you stole some Bitcoin from the mafia and could not cash it. There are some services that can mix Bitcoin to hide their origin.