One way to lock some of the carbon in plant biomass into the soil for a very long time is, paradoxically, by burning it. While most of the carbon in burning vegetation does literally go up in smoke, turning back into CO2, a small fraction — around 1% to 5% or so — of it turns into ash and charcoal, collectively known as black carbon or pyrogenic carbon.
Once formed, this black carbon can stay in the soil for a very long time (half-life measured in thousands of years) since, being essentially inorganic elemental carbon, it is not easily broken down by microorganisms. Some of it can also get transported by air and/or rivers into lakes and seas, where it can become locked up in sediments for even longer times.
For instance, to quote Forbes, Raison & Skjemstad, "Formation, transformation and transport of black carbon
(charcoal) in terrestrial and aquatic ecosystems", Science of the Total Environment 370 (2006), pp. 190–206 (PDF):
"BC [= black carbon] can comprise up to 40% of the OC [= organic carbon] in terrestrial soils and between 12% and 31% of the OC in deep ocean sediments, and has radiocarbon ages in soils in excess of thousands of years. Hence, BC appears to have a significant half-life, in the order of thousands of years. This relative inertness means that the projected <3% of the carbon converted to BC during forest, savanna and grassland fires, must be considered a significant component of the global carbon cycle with a very slow turnover."
In recent years, there's been increasing interest in the deliberate conversion of biomass into black carbon, often known as biochar in this context. Such artificial charring can achieve much higher conversion ratios than natural burning, on the order of 50% or so, while simultanenously allowing the rest of the biomass to be converted e.g. into biogas and/or directly into energy. The resulting biochar can then e.g. be mixed into farm soil (where it can apparently improve water retention and pH and otherwise improve the soil quality), or it could potentially be dumped into the ocean for very long-term storage.
All this makes biochar production a very attractive proposition. It's almost an environmental engineer's dream come true — a power plant / biogas generator with a negative net CO2 emission rate, effectively burning the hydrogen in hydrocarbon biofuel for energy while locking down the carbon into an inert form that — as icing on the cake — can then be sold as soil improvement material. Of course, as usual with emerging technologies, it's not entirely free of practical problems, but it does show promise.
Ps. Of course, there are also other mechanisms by which carbon in biomass can become locked down for long periods. For example, in peat bogs, the dead moss and other vegetation does not decay normally due to the low pH and lack of oxygen, but rather accumulates as peat. This can also sequester the carbon in it for thousands of years — assuming, of course, that no pesky humans come along to dig it up and burn it.