The .deps.json can specify relative path for any asset. The directory portion of that path is ignored for normal assemblies which are part of the app though.

Repro:

dotnet new console
dotnet add package Newtonsoft.Json
dotnet build

Now in the bin/Debug/netcoreapp3.0 create a sub directory and move the Newtonsoft.Json.dll into it.
Edit the app.deps.json to point to sub/Newtonsoft.Json.dll like this:

{
  "runtimeTarget": {
    "name": ".NETCoreApp,Version=v3.0",
    "signature": "6596ed3d155c0211dab1fd90ba9d71b725c973ba"
  },
  "compilationOptions": {},
  "targets": {
    ".NETCoreApp,Version=v3.0": {
      "Newtonsoft.Json/12.0.1": {
        "runtime": {
          "sub/Newtonsoft.Json.dll": {
          }

Run the app via dotnet app.dll.

Expected:
The host should be able to find the Newtonsoft.Json.dll since it exists in the right relative path.

Actual:
The host fails to find the file, and it fails with error like this:

Error:
  An assembly specified in the application dependencies manifest (app.deps.json) was not found:
    package: 'Newtonsoft.Json', version: '12.0.1'
    path: 'sub/Newtonsoft.Json.dll'

Which is very misleading, as the path contains the subdirectory, but the host doesn't use it to look up the file. This can be observed in the trace:

Processing TPA for deps entry [Newtonsoft.Json, 12.0.1, sub/Newtonsoft.Json.dll]
  Considering entry [Newtonsoft.Json/12.0.1/sub/Newtonsoft.Json.dll], probe dir [], probe fx level:0, entry fx level:0
    Local path query did not exist F:\AppModel\repro\DepsJsonRelative\bin\Debug\netcoreapp3.0\Newtonsoft.Json.dll