Lithium battery charging-undervoltage
I also know that charging a lithium ion battery involves a constant current and constant voltage phase.


It usually does, but it's not necessary. That's the way commercial chargers work, to get the fastest charge while staying within the no-damage parameters.

One common regime that chargers use is to charge to 4.2v, then turn off until the voltage has fallen to 4.1v, then recharge to 4.2v. 

For my money, 'providing enough charge over time' to keep the cell at 4.1v would be kinder if that charge was delivered steadily and the cell never exceeded 4.1v, than if it was provided in bursts and the cell cycled between 4.1v and the higher more damaging 4.2v. The first option is of course a continuous trickle charge.

However, I'm not a battery manufacturer, and I've yet to find data from any of them that discusses longevity under sub-maximum voltage trickle charge conditions. An immense amount of effort has been put into characterising rechargeable cells to get fastest charge rates and largest usable capacity (which, let's face it, is where the volume and the money is), and rather less into using them more gently.

To your specific charging conditions of 4v 100mA. If 100mA is less than the battery's max charge current, then your CI phase will be OK. Once the cell gets to 4v, the charging current will fall. I expect it would fall to essentially nothing. 

I would risk keeping it on CV at 4v indefinitely, taking appropriate precautions to mitigate fire risk. You might be tempted to do the same. You will not find any reputable sources that will tell you this is OK. I will not be responsible for your cells if you do this, and find they degrade more quickly than you hoped. 

It would be interesting for someone, perhaps you, to test a few cells with differing lower voltage trickle charge regimes and report the results, perhaps quarterly over a five or 10 year period. I've considered it, but am unlikely to get around to it.