Recoverable and non-recoverable are not two kinds of depreciation. They are the same subtraction under two different policies. Where the policy settles losses at replacement cost, the depreciation withheld from the first payment can be claimed afterwards, and is called recoverable. Where the policy settles at actual cash value, the depreciated figure is the entire entitlement and there is nothing further to claim, which is what "non-recoverable" describes. The label on an estimate is therefore reporting which policy was bought, and a policyholder who sees "non-recoverable depreciation" on a line item is being told that money is not coming, not that a step is outstanding. The same word can also appear on a replacement cost policy for particular items the policy settles on an actual cash value basis regardless, which is common for contents and outbuildings.
Claiming it is a supplemental claim, and the evidence is the finished work rather than the intention to do it. The insurer reopens the file and pays the balance on proof that the repair or replacement happened, which in practice means the contractor's final invoice showing the actual cost, receipts for materials or replacement items, and frequently photographs of the completed work. Two mismatches show up here. If the job came in below the estimate, the recoverable amount is generally reduced to the actual cost, so the withheld figure is a ceiling rather than a promise. If the job came in above it, the overage is a separate conversation with the adjuster and is not automatically paid out of the withheld amount.
There is a deadline, and it is in the contract rather than in the law. The Texas Department of Insurance's guidance to homeowners states the position without giving a number, because there is no general one: "You usually must complete repairs within a certain period of time. Ask your agent or adjuster if you're not sure." A policyholder who cannot fund the work up front, who is waiting on a contractor after a widespread disaster, or who is deciding whether to repair at all, is running against a clock they have to look up in their own policy. That is the single most common way recoverable depreciation is lost.
Texas adds a second, independent condition, and it is one nothing else on this site covers. Section 707.002 of the Texas Insurance Code provides that "a person insured under a property insurance policy shall pay any deductible applicable to a first-party claim made under the policy." Section 707.004 then gives the insurer an enforcement tool: an insurer issuing a property policy with replacement cost coverage "may refuse to pay a claim for withheld recoverable depreciation or a replacement cost holdback under the policy until the insurer receives reasonable proof of payment by the policyholder of any deductible applicable to the claim." The statute then says what counts, which is the useful part: "a canceled check, money order receipt, credit card statement, or copy of an executed installment plan contract or other financing arrangement that requires full payment of the deductible over time." Note the last item. A policyholder who genuinely cannot pay the deductible in one go is not shut out, provided the arrangement requires full payment over time. This is a condition separate from the completed-work condition, so in Texas a policyholder can have finished the roof and still not be paid because the deductible evidence is missing.
The same Texas legislation attached a criminal offense to the other side of that transaction. Business and Commerce Code section 27.02 requires a 12-point boldface notice on any contract for goods or services of $1,000 or more that is reasonably expected to be paid from property insurance proceeds, and makes it an offense for the seller to pay, waive, absorb or otherwise decline to collect the deductible, or to provide an offsetting rebate or credit, without the insurer's consent.
If there is a mortgage, the money may not come to the policyholder at all. On a repair claim where a balance is owed, the insurer commonly issues the check jointly to the borrower and the mortgage servicer, and the servicer releases funds as the work progresses. The Texas Department of Insurance describes both halves of that process: the homeowner endorses the check and sends it to the mortgage company, which "will deposit the check and release money to you as the work is done", may first ask for a list of the work, cost estimates, information about who is doing it and timelines, and, once it has that information, "must release all or some of the money to you within 10 days." That is Texas's rule and other states differ, but the shape generalizes: a second payment on a large loss can be held by the lender on the lender's own schedule, which is a timing problem a homeowner paying a contractor in stages has to plan around rather than discover.