Blockchain has the records the of all transactions that has ever happened since its genesis. Bitcoin blockchain don't maintain the balance of transactions, rather it maintains the UTXOs account. An address has the ability to spend transaction which were sent to it.
A user of the particular address cannot just enter any arbitrary amount to send. The UTXOs is the proof that an address hasthe specific number of bitcoin against the adress, and if the user tries to send more than what he has in the address, then such a txn would be considered invalid by the network.