The crucial question is what they do with it. As a museum piece, it's not really dangerous. If they open it up, bad things can happen.
This answer assumes that we're talking about a two-stage thermonuclear device. This has a couple of main components: a primary fission charge, a secondary fission and fusion charge, an interstage, and a tamper. The primary fission charge goes off first, compressing the secondary fission charge, which then further heats and then compresses the fusion charge. The interstage and tamper ensure that this whole delicate operation goes off exactly as planned - the timing and geometry have to be just so for it to work.
The tamper is the critical part from a long-term safety perspective:
For the secondary to be imploded by the hot, radiation-induced plasma surrounding it, it must remain cool for the first microsecond, i.e., it must be encased in a massive radiation (heat) shield. The shield's massiveness allows it to double as a tamper, adding momentum and duration to the implosion.
Essentially, in addition to its other jobs, the tamper acts as a huge radiation shield. Though it contains the actual blast for only a crucial millisecond, it can contain the natural decay of the bomb components with ease. It helps that unlike a boosted fusion device (which uses short-lived but highly energetic tritium), this bomb can use stable lithium deuteride fusion fuel. Fission fuels are generally speaking relatively stable over the long term. So as long as you keep the bomb in its original packaging, so to speak, it should be quite safe.
However, if you rip it open and start tinkering with its guts, bad things can happen. Plutonium, in particular, has been linked to problems when radioisotope thermoelectric generators using it have been salvaged and then opened by damage or tampering. Per WP,
The alpha radiation emitted by either isotope [of plutonium] will not penetrate the skin, but it can irradiate internal organs if plutonium is inhaled or ingested. Particularly at risk is the skeleton, the surface of which is likely to absorb the isotope, and the liver, where the isotope will collect and become concentrated.
You should not eat nuclear bomb parts.
If you're opening the bomb up, though, chemical toxicity is a major threat. The tamper is composed of depleted uranium (U-238) which, although not a major radiological hazard, is direly toxic and a fire hazard. (In addition to being flammable, it's brittle, and the resulting dust has a charming habit of spontaneously igniting.)
There's also the interstage, which is composed of... well, nobody in the public domain really knows. But according to DoD documents, it's also toxic. Lithium deuteride, not to be left out, reacts violently with water to create caustic lithium hydroxide, and is highly flammable to boot.
So the upshot is: as long as you don't touch the bloody thing you should be safe from the radioactive materials inside. If you don't know what you're doing and open it up, it'll be a race between the various nasty, nasty things inside to see what does you in first. (My money's on the lithium fire. Those things are tough to put out if you're not expecting them.)