In HubSpot, under Contacts > Contacts Settings > Company Properties, you can choose to sync company Lifecycle Stage to contacts. When enabled, this feature will adjust the Lifecycle Stage of all contacts under the same company in HubSpot.
This setting will take the Lifecycle Stage on the Company as it is moved down the funnel, and apply the change on the associated contacts. For example, if there are two contacts in a company, one with a Lifecycle Stage of Lead and one with a Lifecycle Stage of Marketing Qualified Lead, and the Company's Lifecycle Stage is set to Opportunity, both the contacts' Lifecycle Stage will be subsequently changed to Opportunity. Please note that if a change in Lifecycle Stage up the funnel occurs, such as from Customer to Lead, this will not result in a change to the Contact's Lifecycle Stage as a Contact's Lifecycle Stage first needs to be cleared before they can be moved backwards up the funnel.
Note for Salesforce Integrated users:
Any changes made to a contact's Lifecycle Stage by the Automatic Lifecycle Stage Transitions setting (in HubSpot, Account Menu > Integrations > Salesforce Settings) will be applied to all contacts under the company in HubSpot. Contacts in Salesforce must still be attached to Opportunities via the Contact Roles section, as Accounts associated to Opportunities will not be read by HubSpot.