Make sure that you include the $1 in gross income on your tax return, being as it is an "undeniable accession[] to wealth, clearly realized, and over which the taxpayer[] ha[s] complete dominion". Commissioner v. Glenshaw Glass Co., 348 US 426, 431 (1955). See also 26 USC § 61(a).
Now, you might say, assuming that the $1 was merely lost as opposed to abandoned, your title to it cannot be defended against the true owner and if she should reappear, you would be obligated to return the money. In light of that fact, have you really realised an accession to wealth? It turns out the answer is "yes", you have, because it does not matter whether your title is good against the whole world; "[q]uestions of federal income taxation are not determined by such 'attenuated subtleties'". James v. United States, 366 US 213, 216 (1961) (internal citation omitted). Indeed, "in the absence of [an] unlikely ... demand for the money's return, [the taxpayer] could enjoy its use as fully as though his title to it were unassailable". Rutkin v. United States, 343 US 130, 136 (1952).