I recently encountered problems opening form in the InfoPath 2013 filler after installing 2016 from Office 365. Here's the error message I received:

 While I performed prerequisites to install InfoPath 2013 with Offie2016, I was still unsuccessful. Here are some actions I attempted to resolve the issue:

• Add /">https://<server>/ to your local intranet zone in Internet Explorer
• Delete temporary internet files
• Delete local InfoPath cache
• Repair/Reinstall Office 2016 and InfoPath 2013

One action I did as a workaround is to open the form in template Design --> Choose File --> Choose Form Options --> Choose Security and Trust --> Choose Full Trust radio button

 Once this is applied, I was redirected to InfoPath asking credentials and after login I was able to view the form. But if I open any InfoPath file that should connect directly to our site/server it would automatically fail and deny permission

Solution: It sees that Internet Explorer doesn't register my credentials when I open a form which is why InfoPath denies access

• Deleted Temporary Internet Files in Internet Explorer

• Deleted InfoPath Cached Files in y local machine (in my case it's under C:\Users\Peter Russy Alfafara\AppData\Local\Microsoft\InfoPath

• Before login, I ticked "Remember me next time" check box

By doing these steps, I am now able to open any form from our website.