Can conservatorships be assigned to a person with no assets? If the person had assets at the time of filing, but not at the hearing date, could it still be assigned?
Normally someone would simultaneously seek a conservatorship and a guardianship, or only a guardianship in such a case. And, of course, a guardianship could be sought without management of property being an issue.
Having a guardian and not a conservator, in the case of someone with few assets, is basically the same as having a guardian and a conservator. The guardian would normally have the powers necessary to manage the protected person's small estate.
In making a conservatorship appointment, the focus is usually on the capacity of the would be protected person, and not on that person's current assets.
For example, a conservator might primarily be involved in applying for government benefits (Medicaid, Medicare, Social Security, means tested welfare like food stamps and SSI, VA benefits, etc.) or past employment benefits (e.g. pensions), or legal action (e.g. a personal injury suit or probate lawsuit over an inheritance) that could improve the protected person's situation, rather than upon the protected person's current situation. Alternately, the protected person might have a regular source of income which to the Court appears is not being suitably managed, leading to periodic destitution.
There would need to be some reason to think that if the person currently has not assets that they might gain assets in the future by some means, but a current lack of assets wouldn't be dispositive. Someone who is currently destitute could still have a conservator appointed for them.