If by "benefits" you are referring to the High Deductible Health Plan (HDHP), you can make contributions for those months you are covered by the plan, but you can make that contribution up until the regular due date of your tax return. You do not have to be covered by the plan at the time you actually make the contribution.
You do not have a "family HSA," you have family HDHP coverage that permits you to contribute to an HSA subject to the contribution limit for having family HDHP coverage. The amount an individual under age 55 with family HDHP coverage and contribute for 2019 $7,000 / 12 = $583.33 for each month that the individual is covered by the family HDHP coverage on the first of the month. So if the last day of your HDHP coverage is July 31, you will have been covered for the first 7 months of the year, allowing you a total contribution for 2019 of $4,083.33, split in any manner between payroll deductions and personal contributions. What you take out of the HSA is irrelevant. If you obtain other HDHP coverage later in 2019 (by December 1) or you extend your current HDHP coverage under COBRA, you'll be able to contribute more since you'll have HSA-eligible coverage for additional months of 2019.
