In a stock exchange notice today (14 December), ADIG's board said it believed a managed wind-down would be in the "best interests of shareholders as a whole".
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Investors will be able to vote on the proposals at the trust's annual general meeting on 27 February 2024.
According to data from the Association of Investment Companies, ADIG is currently trading at a 31.4% discount.
Under the board's proposals, shareholders would have roughly £115m returned in the first half of 2024 at, or close to, NAV, it said.
The remainder will then be paid to shareholder in two tranches - which could take up to ten years - as these depend on ADIG's private markets portfolio reaching maturity.
ADIG said the first tranche is expected to return £107.3m, with this section of the portfolio maturing between 2024 and 2027. It added the capital will be paid back to shareholders in a "timely manner as the investments mature".
The second tranche will be worth around £81.5m, comprising the remainder of the private markets portfolio, which is expected to mature between 2029 and 2033.
If the proposals are approved, ADIG would stop making new investments and the board would seek to reduce ongoing costs.
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The trust's debt arrangements, comprising secured bonds with a par value of around £16.1m, will also be repaid in 2024, if the proposals get the green light from shareholders.
ADIG's board added it does not intend to proceed with the £35m tender offer revealed on 26 October.
Winterflood analyst Elliott Hardy said the winding down proposals represent a "continuation on the trend of sub-scale funds with persistent discounts seeking corporate action to realise value for shareholders".
He commended the board for taking this type of action but argued the process is likely to be "more complicated for a fund with a significant proportion of assets in private markets", as asset realisation timelines are restricted.
He continued: "Current market conditions appear particularly challenging in this context, as demonstrated by low transaction volumes. That said, as investors get more clarity on the future path of rates, significant dry powder sat waiting in private markets may ease such pressures, enabling ADIG to realise assets for shareholders in a more timely and, crucially, value accretive (rather than detractive) manner."