There are certain portions of one's financial information that will likely fall into the realm of the Death Envelope. However, for much of this information, I suspect it falls more into the class of "reference material", and will likely be stored in a fashion more readily accessible than a Death Envelope, although you will likely still want some degree of security for it.
When considering this area of your life, the main question to ask is, "Can I be hurt badly if this information is compromised?" For example, your bank account statements, while somewhat sensitive, are unlikely to lead to an immediate risk to your bank account. Your online banking login information, however, is.
Effectively, any information that might be sufficient to allow a criminal to access an account, or financial service should be stored in your Death Envelope, assuming you'd like your next of kin to have access to it.
As well, your ATM PIN number is something you don't want a criminal to have access to, but you may wish your family to have. In fact, my research has led me to believe that this may be one of the more important areas that you should address when considering the possibility of your death. Given the relatively high possibility that your accounts may be frozen for some indeterminate period of time following your death, it may be necessary, possibly even vital, for your immediate heirs to access some "operating cash" quickly, likely via an ATM, should you suffer a fatal occurrence.