Take Canada.
The PM - Papineau
The defence minister - Scarborough South West
Finance Minister - University - Rosedale
Even the Speaker, who stands for the Majesty, is a member of the House - Hull Aylmer.
While Cabinet members are, typically, given safe seats to run, cabinet members can and do lose their seat effectively ending their ministry.
In a strong presidential system, like the US, the "ministers" (i.e.secretaries) are not in fact elected. But, not only are they approved by Congress, but they serve on behalf and on the whim of the President who is elected.
The fount of executive authority is solely in the hands of the President, who merely delegates his authority (who have no power of their own) to the cabinet members and (except for the VP) can fire them at any time.
The President holds all the executive power and the voters pick him.
The EU commissioners are not elected and the Commission president is not elected