HubSpot "Yes/No"-style fields can sometimes be confusing, so we'd like to discuss and clarify some of this functionality.
For HubSpot Opt-Out fields (whether the global Opt-Out or those created from Subscriptions), the field will normally only have a value of true (for having Opted Out), or blank. When a new record is created it will be blank, and this is assumed by HubSpot to be Opted In. The only case where a record may have a false value is in the case where someone has Opted Out and then followed the process to Opt In again (which sets the field to true, and then updates it to false). This is normally only a fraction of a percent of all records seen in a HubSpot system though, if any.
Since we normally map an Opt Out field to a corresponding target "Do Not Allow" field, many clients want to see the blank HubSpot value converted into a false value in the target system, as they do not necessarily make the same assumptions about blank values. We can accommodate this and most other requests, but this all depends on how you will interpret the values inside the target system.
However, for other created True/False (Yes/No) fields, they are more traditionally formatted in that they can be true, false, or blank, and will have a default false value when a new record is created. For these fields, we typically look to mirror the data values, so that we copy any of true, false, or null/blank values to the target system.
We can alter our integration maps to suit your purposes if you'd like them to copy in different ways. Keep in mind that when we map a field to sync, it must copy a value to the target field. So there may be cases where a change has happened you do not expect. You may also wish to have us do pre-checks against existing data for some of these fields and attempt to write the same value back in under certain circumstances. This all depends on how you will treat true, false, and blank field values internally in the target system.
If you have any questions or doubts as to how your data will be synced in the above or other cases, please contact your Developer and we will be glad to review it with you!