It depends on the agency funding the grant, so it is best to check with the Grants Office. The Grants Office keeps records of all contacts with funders and should be the central clearing house for all proposals, so we appreciate hearing from you whenever you are considering submitting a proposal. Most faculty members who are preparing research proposals will be working with the Grants Accountant in Fiscal Affairs to develop their budget and to arrange for accounts to be set up once awards are made. All proposals need to be vetted by an institutional approval process, with top administrators signing off on the Grants Referral Sheet, so you should allow for several days to complete this process.
If the proposal is more institutional in nature (with a broad institutional impact, or in support of the strategic plan, such as a program administered by a center or a program instituted by an administrator), the Grants Office will help the Principle Investigator to craft the proposal, steward it through the institutional approval process, and ultimately submit the proposal. In many cases, these types of proposals may be submitted by the ECSU Foundation. In such cases, the fiscal contact is the ECSU Foundation's accountant, who will set up the account and arrange for money to be withdrawn from it.
In many cases, the funds for a successful grant application will be sent with the check made out to the University or the ECSU Foundation. In other cases, such as federal awards, the money may be electronically transferred to the appropriate account or deposited by direct deposit. Depending on whether the University or the Foundation applied on behalf of your proposal, check with the respective accountant to review expenditures and determine balances.