Since CEF don't normally issue or redeem shares, dividend reinvestments must be made by purchase in the open (secondary) market, either by the fund's dividend reinvestment agent, if held directly at the fund or registered in your name and participating in its DRIP, or by the broker, it the CEF shares are held there in street name.

The latter being the more common circumstance, the broker on or shortly after the payment date for those who are enrolled in the broker's reinvestment program, buys shares in the open market, aggregating all the cash distribution from the fund owed to reinvestors, each reinvesting shareholder being charged the average purchase price and usually without commission.

Since the broker is the shareholder of record (owner) for all the shares of a CEF in street name, allocating whole and partial shares to reinvestors and distribution cash  amounts for those not reinvesting, is simply a bookkeeping matter.  If your shares are at a broker, you have elected his reinvestment program  and the monthly distribution will only purchase a partial share, you should get that partial share credited to your account.

An interesting point wrt CEF is that, since new shares are not normally issued except when the CEF market price is above NAV, an agent is involved to purchase the fund's DRIP shares.  His fee is charged to all shareholders, reinvesting or not, as a fund expense, and the investors in the CEF's DRIP are charged prorata commission fees when the agent buys shares in the open market.  Here is the normal arrangement for CEF DRIPs

The Fund offers a dividend reinvestment plan (the Plan) pursuant to which shareholders may elect to have dividends and capital gains distributions automatically reinvested in common shares (the Shares) of the Fund. You may elect to participate in the Plan by completing the Dividend Reinvestment Plan Application Form. If you do not participate, you will receive all distributions in cash paid by check mailed directly to you by PFPC Inc. as dividend paying agent. On the distribution payment date, if the net asset value per Share is equal to or less than the market price per Share plus estimated brokerage commissions then new Shares will be issued. The number of Shares shall be determined by the greater of the net asset value per Share or 95% of the market price. Otherwise, Shares generally will be purchased on the open market by the Plan Agent. Distributions subject to income tax (if any) are taxable whether or not shares are reinvested.

If your shares are in the name of a brokerage firm, bank, or other nominee, you can ask the firm or nominee to participate in the Plan on your behalf. If the nominee does not offer the Plan, you will need to request that your shares be re-registered in your name with the Fund's transfer agent, PFPC Inc. or you will not be able to participate.

The Plan Agent's service fee for handling distributions will be paid by the Fund. Each participant will be charged their pro rata share of brokerage commissions on all open-market purchases.

 Probably more than you wanted (g)  Best wishes