clr.dll causes 800703e9 on Microsoft .NET 4.6.1

When using a DLL that works fine in a .NET-based Windows app in Excel 2013, it crashes the clr.dll:

Application: EXCEL.EXE
Framework Version: v4.0.30319
Description: The process was terminated due to an internal error in the .NET Runtime at IP 6F033A0F (6EDA0000) with exit code 800703e9.

Faulting application name: EXCEL.EXE, version: 15.0.4833.1000, time stamp: 0x573ac30d
Faulting module name: clr.dll, version: 4.6.1076.0, time stamp: 0x56d7a0ff
Exception code: 0x800703e9
Fault offset: 0x00293a0f
Faulting process id: 0x10d4
Faulting application start time: 0x01d1dceab78fdb9a
Faulting application path: C:\Program Files\Microsoft Office 15\root\office15\EXCEL.EXE
Faulting module path: C:\Windows\Microsoft.NET\Framework\v4.0.30319\clr.dll
Report Id: 1b887d31-48de-11e6-bbcc-005056c00008

The computer has VSTO 2010 installed on top of Windows 7 with all updates applied.

After upgrading to 4.6.2, the crash remained:

Application: EXCEL.EXE
Framework Version: v4.0.30319
Description: The process was terminated due to an internal error in the .NET Runtime at IP 57F3288A (57C80000) with exit code 800703e9.

Faulting application name: EXCEL.EXE, version: 15.0.4833.1000, time stamp: 0x573ac30d
Faulting module name: clr.dll, version: 4.6.1532.0, time stamp: 0x56e76357
Exception code: 0x800703e9
Fault offset: 0x002b288a
Faulting process id: 0x12c4
Faulting application start time: 0x01d1dcf3ff640774
Faulting application path: C:\Program Files\Microsoft Office 15\root\office15\EXCEL.EXE
Faulting module path: C:\Windows\Microsoft.NET\Framework\v4.0.30319\clr.dll
Report Id: 6b1fe8ad-48e7-11e6-ae61-005056c00008

On other devices running 4.5.2 the problem does not occur. It is either PC bound or .NET version bound.

Does anyone know what might trigger this internal error of clr.dll?

Merits go to Hans Passant. It was indeed a very nasty stack overflow occurring under some conditions.