This source states that there are Barr bodies in 0-4% of males.
Why isn't it complete 0%? why some males loose their only X chromosome? How does then their body compensates for those genes which are inactivated?
To understand how the X inactivation can occur in, it requires a bit of understanding of how Barr bodies come about.
The main key players to keep in mind are (From 1):
From 2, Here is a general diagram of how X-inactivation occurs.
X-inactivation requires first, count how many X chromosomes are present (n). Then, the (n-1) number of X chromosomes are inactivated. The choice for which gets inactivated is largely random.
Therefore, if a male has multiple X-chromosomes (as in the case of Klinefelter syndrome) then X-inactivation would occur in males. However, there is also the case that erroneous counting may lead to the inactivation of the only X chromosome in males early in a developing embryo. But this is lethal, and the embryo would die.
More about Kleinfelter Syndrome can be found here: Klinefelter syndrome