L2 while H1 extension is pending with USCIS

[kaanam]

Hi All,
I had applied for my H1 extension and the status is "Initial Review". While the case is pending with USCIS, I have to travel to India in between . Can I go for a new L2 stamping while my H1 is still pending? Or should I get my H1 invalidated and then go for L2 stamping? If I get my H1 invalidated and go for L2 stamping, will my stay in US after my H1 expired be considered illegal since I am getting my H1 invalidated after reaching India? Do I need to carry any supporting docs when I go for L2 stamping?

Thanks in advance.

[kabkaba]

There are two parts to H1 petition, extension of work authorization and extension of status. The extension of status part may get voided when you leave the US while it is pending. What Visa you apply for while abroad does not matter.
If you return to US in L2 status while the H1 petition still remains pending, you will not be able to work without an L2 EAD. But, if H1 petition gets approved in the meanwhile with extension of status, your status will change to H1 because of last action rule. You will then have to maintain H1 status by working for the H1 employer.
If H1 petition gets approved while you are abroad, you will have a choice to return in L2 or H1 status (by obtaining the corresponding Visa). You will then have to maintain whichever status you return in.

Do you want to be able to work after returning? If so, upgrading the H1 petition to premium and then applying for H1 Visa while abroad is advisable.

[kaanam]

I am ok not working too. Would there be any problem when I go for L2 stamping since I have an ongoing case with USCIS? If I invalidate my H1 before going for L2 stamping, would my stay for the period after the H1 expired be considered illegal?

[kabkaba]

If your I-94 has already expired and you leave the US, that itself can void the extension of status part of the petition. IF petition is approved without extension of status, your stay beyond the I-94 will be illegal. Whether you apply for any other Visa while abroad does not matter in this context. Better to upgrade to premium, get extended I-94 and then leave the US.