Is there a way to get an iPhone 6s Plus working when the battery has completely died?

iPhone 6s Plus or iPhone 6?

iPhone 6S is 6 years old, which also affects the battery life, that may be the cause of the problem.

Having the battery replaced by Apple or an Apple Authorized Service Providers may resolve the issue.

Have an iPhone 6S here, in normal use it's fine, but it got really hot only during the last update to iOS 15.

Have the battery replaced by an Apple Authorized Service Providers (about 12 weeks ago), because now it is still possible.

For older iPhone type is a bit trickier, I don't see any older iPhone type in the list, 

See here: https://support.apple.com/iphone/repair/service/battery-power

If you are going to replace the battery, by Apple or an Apple Authorized Service Providers read this Apple article:

Get your iPhone, iPad, or iPod touch ready for service              

https://support.apple.com/en-us/HT201557

You can try putting on the charger for 30 minutes and doing a forced restart while it is still connected to power.