I would choose something closest to option #1: do not put the furlough hours themselves on the balance sheet. Track the required hours separately.
A furlough day is not normally an asset because you do not possess something with monetary value that will later be consumed. It is also not an ordinary liability in your personal accounts because you do not owe somebody money. Rather, your employment agreement requires you to work fewer paid hours.
Suppose you normally earn $2,000 during a pay period but, because of furlough hours, earn only $1,800. Your books should record the $1,800 of income actually earned, rather than recording $2,000 of income followed by a fictional $200 “furlough expense.”
That distinction is important:
Expense≠income you never earned.\text{Expense} \neq \text{income you never earned}.
The $200 represents foregone income, not money that came into your possession and was subsequently spent.
I would therefore maintain a simple nonfinancial schedule such as:
Required furlough: 120 hours
Furlough taken: 32 hours
Remaining obligation: 88 hours
Each time you take a furlough day, update that schedule and let the reduced paycheck appear naturally in GNUCash.
If you particularly want the information accessible from GNUCash, you could use transaction descriptions, notes, scheduled transactions, or another memorandum-style tracking mechanism without treating the hours as dollars in your financial statements. For example, the paycheck description might contain “8 furlough hours this period.”
You could also calculate the economic effect separately:
Foregone income=furlough hours×normal hourly compensation.\text{Foregone income} = \text{furlough hours}\times\text{normal hourly compensation}.
That can be useful for budgeting, but I would treat it as management information rather than an accounting transaction.
So I would use GNUCash to record the financial consequence—the lower income—and a separate hours ledger to document compliance with the union contract. Trying to force furlough hours into asset or liability accounts mixes units (hours and dollars) and makes the financial statements less meaningful rather than more accurate.