  It is widely assumed that there exists a simple transformation from the It\^o
interpretation to the one by Stratonovich and back for any stochastic
differential equation of applied interest. While this transformation exists
under suitable conditions, and transforms one interpretation into the other at
the price of modifying the drift of the equation, it cannot be considered
universal. We show that a class of stochastic differential equations,
characterized by the presence of absorbing states and of interest in
applications, does not admit such a transformation. In particular, formally
applying this transformation may lead to the disappearance of some absorbing
states. In turn, this modifies the long-time, and even the intermediate-time,
behavior of the solutions. The number of solutions can also be modified by the
unjustified application of the mentioned transformation, as well as by a change
in the interpretation of the noise. We discuss how these facts affect the
classical debate on the It\^o vs Stratonovich dilemma.
