Life-expectancy pensions are prescribed by the SIS Act under regulation 1.06(7). Asset-test exempt life expectancy income streams are life-expectancy pensions that have been granted asset-test exemption under the provisions of the Social Security Act 1991, section 9B.
When a life expectancy pension reaches the end of its term any residual amount will normally remain in an unallocated reserve in the fund. That reserve is under the control of the Trustees but it does not belong to any member of the fund. Not even the member who was receiving the pension.
This particular feature of life expectancy pensions is given effect by the following sub-regulation::
SIS Reg 1.06(7)(f) ... the pension does not have a residual capital value; ...
Accordingly, there are no further payments after the pension expires. This what you would expect: after the promised pension payments have been made the contract is fulfilled and the pensioner is not entitled to any further payments.
The trustees can make allocations to members of the fund from the left-over reserve. The taxation treatment of those allocations is described by ITAR 1997 291-25.01. The provisions of that regulation are described here. Depending on its size it may take many years to exhaust that reserve or it may be possible to allocate all of it to fund members in one action.
Consider also that a life expectancy pension can be commuted before it expires. This type of pension can be commuted to a market-linked pension or the assets rolled-out of the fund to purchase a suitable annuity (SIS Reg 1.06(7)(g)(v)). If the pension is an asset-test exempt income stream be sure to consult with Centrelink/DVA before making such a change or risk a hefty penalty.
The commutation value of life expectancy pensions is described here.