Ceratostigma plumbaginoides is a low-growing evergreen subshrub that can serve both purposes.
From the sfgate.com
Likewise lavender, actually a subshrub.
From the philly.com
This sage is a subshrub, a type of perennial that develops woody stems and twigs that can be very long-lived.
From the ocregister.com
Atropa belladonna is a branching herbaceous perennial, often growing as a subshrub, from a fleshy rootstock.
From the en.wikipedia.org
It is an erect, much branched subshrub, 30-60 cm tall with hairy stems and simple, opposite, green leaves that are strongly scented.
From the en.wikipedia.org
Native to the mountain slopes of eastern Asia, but equally at home in our Mediterranean climate, this vigorous subshrub grows quickly to a height of 3 to 5 feet and at least an equal width.
From the sfgate.com
More examples
Low-growing woody shrub or perennial with woody base
A subshrub (Latin suffrutex) is a short woody plant. Prostrate shrub is a similar term.
Undershrub; a small and sometimes sparsely branched woody plant less than 1 m high.
(syn. suffrutex) - plants with an often woody, sometimes fleshy, underground perennating organ and annual flowering stems, often in an adaptation to perennate the plants through periods of drought or through fire.
Somewhat or slightly shrublike; usually a plant with a stem that is woody at the base, but mostly herbaceous.
A low growing plant having a woody base and herbaceous canopy.
A low lying plant that has woody stems.
A plant with more or less woody branches and roots, less woody than a true shrub, but more woody than a perennial herbaceous plant; a small shrub, woody only at the base.