Most countries with significant foreign workforces or student populations do offer dependent visas for spouses and minor children, tied to the primary holder's status and expiring alongside it. Eligibility usually requires proof of relationship, such as marriage and birth certificates, often legalized or apostilled, plus evidence the sponsor can financially support the family and provide accommodation.
What dependents may actually do varies widely. In some countries a dependent spouse gets full or near-full work rights automatically; in others they need a separate work permit or cannot work at all. Children can normally attend school, though whether public schooling is free for them differs. Some countries restrict which visa categories can sponsor dependents in the first place, or set minimum salary thresholds for the sponsor.
Since spouse work rights are often the deciding factor for families, verify that specific point on the immigration authority's website for your visa category rather than assuming. Rules also change periodically, so check dates on anything you read.