Thank you for your question, and for having the wisdom to learn more BEFORE taking any action.
With this being a purely POST-petition
lease, 11 USC §365(g) does not apply. That one provides for post-petition obligations under a rejected lease to be treated as pre-petition claim under the plan. When a lease existed before the BK filing, arrears can be treated as high-priority administrative claims.
As your question implied that you already know, the automatic stay of 11 U.S.C. § 362 is something to scrupulously avoid violating. That includes post-petition debt creditors--even they are prevented from going after the assets of the BK estate to satisfy those debts. In re Bottone, 226 B.R. 290, 297 (Bankr. D. Mass. 1998) (“as long as the Chapter 13 case is pending . . . the automatic stay … restrains postpetition creditors from taking action against property of the estate”) (quoting In re Woodall, 81 B.R. 17, 18 (Bankr. E.D. Ark. 1987)).
That is almost counter-intuitively contrasted with the fact that *discharge* of post-petition debts is not possible in a bankruptcy case.
At first flush, 11 § 541(a)(1)'s definition of the BK estate might sound like almost everything (“. . . all legal or equitable interests of the debtor in property as of the commencement of the case.”). See In re Lankford, 305 B.R. 297, 301 (Bankr. N.D. Iowa 2004) (“All recognizable interests of the debtors or the estate are afforded the protection of § 362(a). But there are some things that are NOT part of the BK estate.
The solution for a Chapter 13 case post-petition debt creditor (regardless of whether it is a lease or some other obligation) is that the postpetition income stream of the debtor is NOT considered property of the BK estate. In re Howell, 311 B.R. 173, 179 (Bankr. D. N.J. 2004) (automatic stay does not preclude estranged spouse from seeking equitable distribution of non-estate property such as exempt property, postpetition earnings, property excluded from the estate, property abandoned by the trustee or debtor surplus). See also Telfair V. First Union Mortgage Corp. (In re Telfair), 216 F.3d 1333 (11th Cir. 2000,) at p. 1340-41.
It could still get complicated because a Chapter 13 Plan pretty much accounts for all of the postpetition earnings, and there might not be any room to execute on anything left over--there usually isn't any. With the time appropriate to this question, I have not found any case law that clarifies how that would be handled. My first line of inquiry would be into whether the discretionary parts of the debtor's budget would need to be adjusted to allow for the collection efforts.