Can on-the-job people move their accounts when they buy a house in a different place?

Of course. Where to work, in what unit, does not affect the migration of registered permanent residence, as long as it conforms to the policy.

Beishangguangshen and Shenzhen are not within the scope of examples ~

For example, if you work in a government unit in city A, but you buy a house in city B, you can move your household registration to city B, as long as city B allows you to enter the house.

For another example, if you work in a government unit in city A, and your original registered permanent residence is in city B, you can also move your registered permanent residence to Gong Hu in city A, as long as Gong Hu of your unit is willing to accept you.

The state does not impose any restrictions on the accounts of public officials, except that serving public officials are not allowed to emigrate (including Hong Kong, Macao and Taiwan), and they will resign once they emigrate. The spouses, children and other immediate family members of public officials can emigrate, but if the whole family emigrates, only public officials, which we often call "naked officials", cannot hold real leadership positions.