I'm trying to search for this thing but I'm unsure what terms to use. I see it a lot in logos. It's where a letter, typically the last, extends down under the word like a thick underline. Sometimes they use it as a background for more text.
Where this device is formed from a capital, it's called a swash and there are many font variants with "Swash Capitals". Originally it was designed to fill the space between letters1, but often now swash capitals incorporate strokes which are far more ornate or elongated than a simple space filler.
In the absence of anything better, the term might easily be applied to the stroke in the illustration.
1 OED, 1918: Printing. Applied to old-style capital letters having flourished strokes designed to fill up unsightly gaps between adjacent letters.