Answer
$I=0.1I_{0}$
Work Step by Step
Yes. There can be negative decibel level. The sound intensity level is a log scale for comparison of sound intensity and threshold of hearing.
Intensity level = $beta$=$10log\frac{I}{I_{0}}$
$I$ being the sound intensity.
Having a negative beta would mean that the sound intensity is lower than the threshold of hearing.
For example,
$-10=10log\frac{I}{I_{0}}$
So,
$I=0.1I_{0}$
