Can one have a case in which an employee for a company performed an
act in malice that caused injury to a party.
Then that party puts forward a criminal case against the employee (for
jail time), but ALSO put forward another case as civil lawsuit to the
company (aiming for monetary damages), for it's lack of oversight &
encouraging the employee's attitude.
The Crown (i.e. the government) prosecutes and controls a criminal case. A civil case is commenced and litigated by a private party. Generally speaking, in this situation, a private party can't initiate or control the litigation of the criminal case.
A private party can ask that the government bring a criminal case, but the government doesn't have to cooperate, and the private party still has no say in how the criminal case in managed.
Often, civil cases are stayed while a related criminal case is pending, but that is a discretionary determination made on a case by case basis by a judge in the civil case. Criminal cases are almost never stayed due to a pending civil case.
It isn't improper to bring a civil case regarding circumstances that are also the subject of a criminal case, however.
If the criminal case results in a conviction, any determinations that were necessary to that conviction are considered proved as a matter of law without any further presentation of evidence or room for appeal, in the civil case, due to a doctrine historically called "collateral estoppel." This simplification of the civil case if there is a conviction is one of the reasons that the civil case is often stayed pending an outcome for the criminal case.