Inventory offers to other avatars are effectively done as a special form of IM.
A result of this is that if your IMs have been capped, any inventory offers to you are silently dropped.
I'm classing this as a bug, as this behaviour may be by design but it is undesirable:
a) in the case of IMs and group notices, you can at least still read these if you enable sending of IMs to e-mail (or view the archived notices in groups) - in the case of inventory offers you can see you received an inventory offer in e-mail but apart from contacting the original sender in the hope they will resend it, you can't get the inventory
b) the sender is not informed that the inventory offer failed, so may believe the person received it - nor is there any way of checking in advance whether the inventory offer would succeed (apart from checking if the person is definitively online, but even online status is not that reliable).
c) if the item offered is no-copy, the item is neither recieved by the recipient, nor returned to the sender if the recipients IMs are capped
d) there are a number of ways in which inventory might be sent whilst offline, and so may fall foul of this - gifts from other avatars, update servers sending out an available update to previous customers, someone using a web-based retailer (e.g. SLExchange) whilst offline etc. In the latter two cases, a potential solution of just indicating that the offer failed to the sender would not be sufficient.
Ideally inventory offers should work differently to IMs and not be capped even if IMs and Group notices are capped.
If you support this bug report, please vote at http://jira.secondlife.com/browse/SVC-2359